Séminaires passés de l'équipe Méthodes Formelles (MF)

Séminaires passés de l'équipe Méthodes et Modèles Formelles (M2F) depuis 2017

Date Orateur Titre
mardi 18 octobre Pierre Ohlmann (University of Warsaw) Infinite duration games, memory, and graphs
In this talk, I will give a broad overview of the field of infinite duration games: why do we care about them, and what are the main open questions. I will then discuss a new approach to making progress on these questions by reducing them to problems about (directed) graphs.
mardi 4 octobre Laurent Doyen (LMF, ENS Paris-Saclay) Stochastic Games with Synchronizing Objectives
We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding stochasticity. The outcome of the game is a sequence of distributions over the states of the game graph. We consider synchronizing objectives, which require the probability mass to accumulate in a set of target states, either always, once, infinitely often, or always after some point in the outcome sequence; and the winning modes of sure winning (if the accumulated probability is equal to 1) and almost-sure winning (if the accumulated probability is arbitrarily close to 1). We present algorithms to compute the set of winning distributions for each of these synchronizing modes, showing that the corresponding decision problem is PSPACE-complete for synchronizing once and infinitely often, and PTIME-complete for synchronizing always and always after some point. These bounds are remarkably in line with the special case of MDPs, while the algorithmic solution and proof technique are considerably more involved, even for deterministic games. This is because those games have a flavour of imperfect information, in particular they are not determined and randomized strategies need to be considered, even if there is no stochastic transitions in the game graph. Moreover, in combination with stochasticity in the game graph, finite-memory strategies are not sufficient in general (for synchronizing infinitely often).
mardi 20 septembre Christoph Haase (University of Oxford) Directed Reachability for Infinite-State Systems
Directed model checking is a bug-finding technique that emerged in the late 1990s, primarily applied to finite-state systems and infinite-state systems with finite quotient graphs such as timed automata. Recent progress in the areas of optimisation modulo theories and arithmetic abstractions of infinite-state systems makes it possible to apply this technique to efficiently (semi-)deciding reachability in inherently infinite-state systems that may even have undecidable reachability problems. In this talk, I will give an introduction to the ideas underlying directed model checking and demonstrate how it can be used to semi-decide reachability problems in large-scale Petri nets. This talk is based on joint work with M. Blondin and Ph. Offtermatt (Sherbrooke, CA)
mardi 24 mai 2022 Michaël Thomazo (INRIA Saclay) Capturing Homomorphism-Closed Decidable Queries with Existential Rules
Existential rules are a well studied ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms. In this paper, we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates. Membership in this fragment is not decidable, but we show via a diagonalisation argument that this is unavoidable.
mardi 05 avril 2022 Bernd Finkbeiner (CISPA Helmholtz Center for Information Security) Model Checking Hyperproperties
Traditionally, most verification efforts have focused on the satisfaction of trace properties, such as that an assertion is satisfied at a particular program location or that the computation terminates eventually. Many policies from information-flow security, like observational determinism or noninterference, and many other system properties including promptness and knowledge can, however, not be expressed as trace properties, because these properties are hyperproperties, i.e., they relate multiple execution traces. In this talk, I will give an overview on recent efforts to develop specification logics and model checking algorithms for hyperproperties. The two principal ideas are the addition of variables for traces and paths in temporal logics, like LTL and CTL*, and the introduction of the equal-level predicate in first-order and second-order logics, like monadic first-order logic of order and MSO. Both extensions have a profound impact on the expressiveness of the logics, resulting in a hierarchy of hyperlogics that differs significantly from the classical hierarchy. Model checking remains decidable for a large part of the new hierarchy. Satisfiability is in general undecidable for most hyperlogics, but there are useful decidable fragments. I will report on first successes in translating these encouraging theoretical results into practical verification tools.
mardi 01 mars 2022 Stéphane Demri (LSV (ENS Paris-Saclay)) Logics with concrete domains: an introduction
In this talk, we present logical formalisms in which reasoning about concrete domains is embedded in formulae at the atomic level. These mainly include temporal logics with concrete domains and description logics with concrete domains.
mardi 15 février 2022 Thomas Colcombet (IRIF) Learning Automata and Transducers: A Categorical Approach
We present a categorical approach to learning automata over words, in the sense of the L*-algorithm of Angluin. This yields a new generic L*-like algorithm which can be instantiated for learning deterministic automata, automata weighted over fields, as well as subsequential transducers. The generic nature of our algorithm is obtained by adopting an approach in which automata are simply functors from a particular category representing words to a computation category. We establish that the sufficient properties for yielding the existence of minimal automata (that were disclosed in a previous paper), in combination with some additional hypotheses relative to termination, ensure the correctness of our generic algorithm.
mardi 18 janvier 2022 Bartek Klin (University of Oxford) Orbit-finite-dimensional vector spaces, with applications to weighted register automata
I will discuss vector spaces spanned by orbit-finite sets. These spaces are infinite-dimensional, but their sets of dimensions are so highly symmetric that the spaces have many properties enjoyed by finitely-dimensional spaces.
mardi 14 décembre 2021 Jan Otop (University of Wroclaw) Active learning automata with syntactic queries
Regular languages can be actively learned with membership and equivalence queries in polynomial time. The learning algorithm, called the L^* algorithm, constructs iteratively the right congruence relation of a given regular language L, and returns the minimal DFA recognizing L. The L^* algorithm has been adapted to various types of automata: tree automata, weighted automata, nominal automata. However, an extension to infinite-word automata has been elusive.
mardi 07 décembre 2021 Léo Exibard (ICE-TCS, Reykjavik University) Extending Reactive Synthesis to Infinite Data Domains through Machines with Registers
In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulas or automata over infinite sequences of signals (omega-words), while implementations are represented as transducers. In the classical setting, the set of signals is assumed to be finite.
mardi 30 novembre 2021 Nofar Carmeli (École Normale Supérieure, Paris) Efficiently Simulating a Sorted Array with Conjunctive Query Answers
A sorted list of query answers may be much larger than the size of the input database. If its use-case does not entail going over this list one-by-one, but rather it is needed in order to compute the median, a boxplot, or another task that requires jumping arbitrarily to answers by their indices, computing this entire list is unnecessary and inefficient. In this talk, we inspect the question of when a sorted array of query answers can be efficiently simulated. We call this task ranked direct access and focus on near-optimal time guarantees. We ask in which cases ranked direct access can be achieved with only logarithmic factors as overhead on top of the linear time required to determine whether there is an answer, and the constant time required per accessed answer. Thus, we ask which CQs and orders can be answered with quasilinear preprocessing and polylogarithmic access time. We show algorithms for lexicographic and sum-of-weight orders, and prove conditional lower bounds implying that (under some complexity assumptions) our algorithms capture all tractable cases for self-join-free CQs.
mardi 16 novembre 2021 Christof Löding (RWTH Aachen University) Constructing Deterministic Omega-Automata from Examples by an Extension of the RPNI Algorithm
Learning techniques for deterministic finite automata (DFA) have been developed starting from the 1970ies. The two main settings are the construction of DFA from examples (finite sets of words that should be accepted or rejected by the DFA), and from queries to an oracle. These problems are already well understood for DFA, and various learning algorithms for these two settings exist. Deterministic automata on infinite words define languages of infinite words, and are syntactically very similar to DFA. However, certain key properties of DFA that are used in learning algorithms do not hold for automata on infinite words. Therefore, only few results for learning automata over infinite words have been obtained up to now. In this talk, I present an algorithm for the construction of deterministic omega-automata from examples that is obtained by adapting an algorithm called RPNI from the setting of finite words.
mardi 19 octobre 2021 Alexandra Silva (Cornell University) Concurrent NetKAT: Modeling and analyzing stateful, concurrent networks
We introduce Concurrent NetKAT (CNetKAT), an extension of the network programming language NetKAT with multiple packets and with operators to specify and reason about concurrency and state in a network. We provide a model of the language based on partially ordered multisets, well-established mathematical structures in the denotational semantics of concurrent languages. We prove that CNetKAT is a sound and complete axiomatization of this model, and we illustrate the use of CNetKAT through various examples. More generally, CNetKAT is an algebraic framework to reason about programs with both local and global state. In our model these are, respectively, the packets and the global variable store, but the scope of applications is much more general, including reasoning about hardware pipelines inside an SDN switch.
mardi 12 octobre 2021 Georg Zetzsche (Max Planck Institute) Context-bounded verification of liveness properties for multithreaded shared-memory programs
We study context-bounded verification of liveness properties of multi-threaded, shared-memory programs, where each thread can spawn additional threads. Our main result shows that context-bounded fair termination is decidable for the model; context-bounded implies that each spawned thread can be context switched a fixed constant number of times. Our proof is technical, since fair termination requires reasoning about the composition of unboundedly many threads each with unboundedly large stacks. In fact, techniques for related problems, which depend crucially on replacing the pushdown threads with finite-state threads, are not applicable. Instead, we introduce an extension of vector addition systems with states (VASS), called VASS with balloons (VASSB), as an intermediate model; it is an infinite-state model of independent interest. A VASSB allows tokens that are themselves markings (balloons). We show that context bounded fair termination reduces to fair termination for VASSB. We show the latter problem is decidable by showing a series of reductions: from fair termination to configuration reachability for VASSB and thence to the reachability problem for VASS. For a lower bound, fair termination is known to be non-elementary already in the special case where threads run to completion (no context switches).
mardi 28 septembre 2021 Denis Kuperberg (ENS Lyon) Positive first-order logic on words
I will present FO+, a restriction of first-order logic on words, where letter predicates are required to appear positively. The words considered here are on a powerset alphabet: predicates a(x) and b(x) can be true simultaneously. We will ask a syntax versus semantics question: FO+-definable languages are monotone in the letters (with respect to inclusion), but can every FO-definable monotone language be expressed in FO+ ? On general structures, Lyndon's theorem gives a positive answer to this question, but it is known to fail on finite structures. We will see that it also fails on finite words, by giving a simple counter-example language. This gives a new proof for the failure of Lyndon's theorem on finite structures, that is much more elementary than previous proofs. Finally we will see that surprisingly, FO+-definability is undecidable for regular languages.
mardi 29 juin 2021 Joost-Pieter Katoen ( RWTH Aachen University and University of Twente) Multi-cost Bounded Tradeoff Analysis in MDP
We present a memory-efficient algorithm for multi-objective model checking problems on Markov decision processes (MDPs) with multiple cost structures. The key problem at hand is to check whether there exists a scheduler for a given MDP such that all objectives over cost vectors are fulfilled. We cover multi-objective reachability and expected cost objectives, and combinations thereof. An empirical evaluation using a prototypical implementation on top of the Storm model checker shows the scalability of our approach both in terms of memory consumption and runtime.
mardi 01 juin 2021 Gerco van Heerdt (University College London) Learning Pomset Automata
Abstract: We adapt the L* algorithm to learn bimonoids recognising pomset languages. We then show how to convert between bimonoids and a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids.
mardi 18 mai 2021 Wojciech Czerwinski (the Institute of Informatics, Faculty of Mathematics, Informatics and Mechanics of the University of Warsaw) Reachability in Vector Addition Systems is Ackermann-complete
Complexity of the reachability problem in Vector Addition Systems (VASes) was a long standing problems for a few decades. Very recently two proofs of Ackermann-hardness were obtained independently
mardi 04 mai 2021 Andrzej Murawski (University of Oxford) Verifying higher-order concurrency with data automata
Using a combination of automata-theoretic and game-semantic techniques, we propose a method for analysing higher-order concurrent programs. Our language of choice is Finitary Idealised Concurrent Algol (FICA) due to its relatively simple fully abstract game model.
mardi 27 avril 2021 Mahsa Shirmohammadi (IRIF) Cyclotomic Identity Testing and Application
We consider the cyclotomic identity testing (CIT) problem: given a polynomial f(x_1,...,x_k),
mardi 13 avril 2021 Jan Kretinsky (Technical University of Munich) Learning-based LTL synthesis
In LTL synthesis, the task is to construct a reactive system producing an output stream ensuring a given formula of linear temporal logic is satisfied for any input stream. Recent results on translating LTL to automata open avenues to learning-based approaches and heuristics for such problems. In particular, the automata-theoretic approach to LTL synthesis can utilize not only topological information through standard graph algorithms, but can now also profit from semantic information through learning algorithms. As a result, in many cases an optimal solution can be obtained without any computation; in more general cases, the approach might yield more explainable controllers and scale better.
mardi 30 mars 2021 Thomas Zeume (Ruhr University Bochum) Register Automata with Extrema Constraints, and an Application to Two-Variable Logic
In this talk I will introduce a model of register automata over infinite trees with extrema constraints. Such an automaton can store elements of a linearly ordered domain in its registers, and can compare those values to the suprema and infima of register values in subtrees. We will see that the emptiness problem for these automata is decidable. As an application, I will outline how the satisfiability problem for two-variable logic with arbitrary predicates, two of them interpreted by linear orders, can be decided.
mardi 23 mars 2021 Peter Hines (Université de York) Shuffles, Operads, and Associahedra in Theoretical Computer Science
The use of shuffling together decks of cards as a metaphor for interleaving execution of processes is well-established in computer science, and has allowed for the transfer of concepts and tools from pure mathematics to areas such as the analysis of Race Conditions. This talk aims to demonstrate that, when we extend this intuition and related models to the infinitary case, we find further connections with many topics in theoretical computing. These range from logical models to cryptographic platforms and questions of complexity and computability.
mardi 16 mars 2021 Dmitry Chistikov (The University of Warwick) Subcubic Certificates for CFL Reachability
The context-free language (CFL) reachability problem on graphs, as well as
mardi 02 mars 2021 Nofar Carmeli (ENS) The Complexity of Answering Unions of Conjunctive Queries
We discuss the fine-grained complexity of enumerating the answers to a query over a relational database. With the ideal guarantees, linear time is required before the first answer to read the input and determine its existence, and then we need to print the answers one by one. Consequently, we wish to identify the queries that can be solved with linear preprocessing time and constant or logarithmic delay between answers. A known dichotomy classifies CQs into those that admit such enumeration and those that do not. The computationally expensive component of query answering is joining tables, which can be done efficiently if and only if the join query is acyclic. However, the join query usually does not appear in a vacuum; for example, it may be part of a larger query, or it may be applied to a database with dependencies. We inspect how the complexity changes in these settings and chart the borders of tractability within. In addition, we consider the task of enumerating query answers with a uniformly random order, and we propose to do so using an efficient random-access structure for representing the set of answers. We also prove conditional lower bounds showing that our algorithms capture all tractable queries in some cases. Among our results, we show that a union of tractable conjunctive queries may be intractable w.r.t. random access; on the other hand, a union of intractable conjunctive queries may be tractable w.r.t. enumeration.
mardi 02 février 2021 Stefan Göller (Universität Kassel) Bisimulation Finiteness of Pushdown Systems Is Elementary
It is shown that if a pushdown system is bisimulation equivalent to a finite system, there is already such a finite system whose size is elementary in the description size of the pushdown system. As a consequence, it is elementarily decidable if a pushdown system is bisimulation-finite. This is joint work with Pawel Parys.
mardi 15 décembre 2020 Engel Lefaucheux (Max-Planck Institute for Software Systems) Reachability in dynamical systems with rounding
We consider reachability in dynamical systems with discrete linear updates, but with fixed decimal precision, i.e., such that values of the system are rounded at each step. Given a matrix M in Q^{d*d}, an initial vector x in Q^d, a granularity g in Q_+ and a rounding operation [·] projecting a vector of Q^d onto another vector whose every entry is a multiple of g, we are interested in the behaviour of the orbit O=
mardi 08 décembre 2020 Miguel Romero Orth (Universidad Adolfo Ibáñez) On monotonic determinacy and rewritability for recursive queries and views
Answering queries using views is a classical and well-studied topic in database theory. Some key associated problems are (monotone) determinacy – can the query Q be expressed as a (monotone) function of the set of views? -- and rewritability – can the query Q be rewritten in certain language over the schema of the views?
mardi 01 décembre 2020 Antonio Casares (LaBRI) Optimal transformations of Muller conditions
In this talk, I will present a construction that takes as input a Muller automaton and transforms it into a parity automaton in an optimal way. More precisely, the resulting parity automaton has minimal size and uses a minimal number of priorities among those automata that admit a locally bijective morphism to the original Muller automaton. This transformation and the optimality result can also be applied to games and other types of transition systems.
mardi 24 novembre 2020 Maud Szusterman (IMJ-PRG) Monotone ABPs complexity vs. monotone rank of some explicit polynomials
In this talk, I will introduce a few computational models, known as (algebraic) circuits and formulas, and as branching programs (ABPs). Restricted classes of computation, such as monotone circuits, or non-commutative ABPs, have been investigated through the past decades. In the latter setting, a family of matrices (Nisan matrices) naturally appears, their ranks are related to the optimal size of a circuit computing the target polynomial. Recently, we investigated weak monotonicity (a relaxation of the monotonicity constraint), and found some explicit polynomials for which the weak-non-negative ranks don’t characterize the minimal size of an ABP computing them. The sum of ranks still gives a lower bound on minimal-size computation, and this can be used, for instance, to obtain a quadratic lower bound when computing the elementary symmetric polynomial. Joint work with Hervé Fournier, Guillaume Malod, and Sébastien Tavenas.
mardi 17 novembre 2020 Joël Ouaknine (Max Planck Institute for Software Systems) Holonomic Techniques, Periods, and Decision Problems
mardi 03 novembre 2020 Nathanaël Fijalkow (LaBRI - CNRS) DeepSynth, two years later: what have we learned about program synthesis?
In January 2019 we started the DeepSynth project to understand the use of machine learning for program synthesis. Two years later, I will discuss our current understanding, the ideas we had, and some perspectives.
mardi 20 octobre 2020 Richard Combes (Supelec) Solving Random Parity Games in Polynomial Time
We consider the problem of solving random parity games. We prove that parity games exibit a phase transition threshold so that when the degree of the graph that defines the game has a degree large enough then there exists a polynomial time algorithm that solves the game with high probability when the number of nodes goes to infinity. We further propose the SWCP (Self-Winning Cycles Propagation) algorithm and show that, when the degree is large enough, SWCP solves the game with high probability. Furthermore, the complexity of SWCP is polynomial. The design of SWCP is based on the threshold for the appearance of particular types of cycles in the players' respective subgraphs. We further show that non-sparse games can be solved in polynomial time with high probability. This is a joint work with Mickael Touati. More information at https://arxiv.org/abs/2007.08387
mardi 06 octobre 2020 Igor Konnov (INRIA Nancy) Using TLA+ and Apalache to specify and check the Tendermint light client
TLA+ is a language for formal specification of all kinds of computer systems. System designers use this language to specify concurrent, distributed, and fault-tolerant protocols, which are traditionally presented in pseudo-code. At Informal Systems, we are using TLA+ to specify and reason about the protocols that are implemented in the Tendermint blockchains and Cosmos ecosystem.
mardi 29 septembre 2020 Mikael Monet (Millenium Instititute for Foundational Research on Data) Title: Counting Problems over Incomplete Databases
In this presentation I will talk about various counting problems that naturally arise in the context of query evaluation over incomplete databases. Incomplete databases are relational databases that can contain unknown values in the form of labeled nulls. We will assume that the domains of these unknown values are finite and, for a Boolean query $q$, we will consider the following two problems: given as input an incomplete database $D$, (a) return the number of completions of $D$ that satisfy $q$; or (b) return or the number of valuations of the nulls of $D$ yielding a completion that satisfies $q$.
mardi 15 septembre 2020 Damien Busatto-Gaston (ULB) Monte Carlo Tree Search guided by Symbolic Advice for MDPs
We consider the online computation of a strategy that aims at optimizing the expected average reward in a Markov decision process. The strategy is computed with a receding horizon and using Monte Carlo tree search (MCTS). We augment the MCTS algorithm with the notion of symbolic advice, and show that its classical theoretical guarantees are maintained. Symbolic advice are used to bias the selection and simulation strategies of MCTS. We describe how to use QBF and SAT solvers to implement symbolic advice in an efficient way. We illustrate our new algorithm using the popular game Pac-Man and show that the performances of our algorithm exceed those of plain MCTS as well as the performances of human players.
mardi 08 septembre 2020 Guillermo A. Perez (University of Antwerp) Safe Learning for Near Optimal Scheduling
We formalize the problem of maximizing the mean-payoff value with high probability while satisfying a parity objective in a Markov decision process with unknown probabilistic transition function and unknown reward function. Assuming the support of the unknown transition function and a lower bound on the minimal transition probability are known in advance, we show that in single end components two combinations of guarantees on the parity and mean-payoff objectives can be achieved depending on how much memory one is willing to use.
mardi 30 juin 2020 Helmut Seidl (TUM) When Is a Bottom-up Deterministic Tree Transducer Top-down Deterministic?
We consider two natural subclasses of deterministic top-down tree-to-tree transducers, namely, linear and uniform-copying transducers. For both classes we show that it is decidable whether the translation of a transducer with look-ahead can be realized by a transducer from the same class without look-ahead.
mardi 23 juin 2020 Elena Gutierrez (IMDEA Software Institute) A Congruence-based Perspective on Automata Minimization Algorithms
Getting the deterministic finite-state automaton with the least possible number of states is an essential question in many applications such as text processing, image analysis and program verification and synthesis.
mardi 02 juin 2020 Ana Ozaki (University of Bergen) Learning Description Logic Ontologies
Ontologies have been used to describe knowledge in various domains, in particular, in those related to life sciences. Semi-automating the process of building an ontology has attracted researchers from various communities into a field called Ontology Learning. The process of building an ontology can be divided into two main tasks: finding the relevant vocabulary and the appropriate ontology language, and discovering how the vocabulary should be related using the logical constructs available in the chosen ontology language. In this presentation, I will provide a brief overview of five approaches from the literature which have been proposed to semi-automate the process of building an ontology formulated in description logic (DL), focusing on the second task. I will then present some results on the complexity of learning lightweight DL ontologies in the exact and probably approximately correct learning models from computational learning theory.
mardi 26 mai 2020 Abhishek De (IRIF) A parallel syntax for non-wellfounded proof theory
Proof theory is the study of proofs as mathematical objects in their own right. Infinite proofs (eg. infinite descent proofs) are pervasive in mathematics. A formal way of characterizing such proofs can be done by looking at fixed point logics (eg. mu calculus) from proof-theoretic lenses. Baelde et. al. have proposed an infinitary sequent calculus (i.e. infinitely deep, finitely wide proofs) for linear logic with fixed points (muMALL). In this talk, following a brief history of proof theory and infinite proofs, I will introduce muMALL. However, the sequent calculus of muMALL turns out to be ``too sequential. In order to achieve more liberal cut elimination, we have devised infinets which are proofs nets (à la Curien) for the multiplicative fragment (muMLL). The later part of the talk will focus on infinets and ongoing work on these nets.
mardi 19 mai 2020 Antoine Amarilli (Télécom Paris) Query evaluation on probabilistic data: a story of dichotomies
Query evaluation is the problem of checking if some input data
mardi 05 mai 2020 Thibault Godin (Université de Montpellier, Université de Lorraine) Order problem for automaton semigroups
The class of automaton (semi)groups--that is (semi)groups generated by functions defined using transducers--has been studied since the late 70's as many very interesting (semi)groups arise from it. From a computer scientist point of view it is also very nice because the underlying automaton structure allows to apply known tools, and for instance one can decide if an element represents the identity element using automaton minimization.
mardi 21 avril 2020 Filip Mazowiecki (Max Planck Institute for Software Systems) On polynomial recursive sequences
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is b_n=n!. Our main result is that the sequence u_n=n^n is not polynomial recursive.
mardi 14 avril 2020 Pierre Ohlmann (IRIF) Controlling a random population
Bertrand et al. (2017) introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is decidable and EXPTIME-complete in the adversarial setting, and posed as an open problem the stochastic setting, where the agent is represented by a Markov decision process. In this paper, we show that the stochastic control problem is decidable. Our solution makes significant uses of well quasi orders, of the max-flow min- cut theorem, and of the theory of regular cost functions.
mardi 31 mars 2020 Jérôme Leroux (CNRS, LaBRI) Reachability in fixed dimension vector addition systems with states
The reachability problem is a central decision problem for formal verification based on vector addition systems with states (VASS), which are equivalent to Petri nets and form one of the most studied and applied models of concurrency. Reachability for VASS is also inter-reducible with a plethora of problems from a number of areas of computer science. In spite of recent progress, the complexity of the reachability problem remains unsettled, and it is closely related to the lengths of shortest VASS runs that witness reachability. We consider VASS of fixed dimension, and obtain three main results. For the first two, we assume that the integers in the input are given in unary, and that the control graph of the given VASS is flat (i.e., without nested cycles). We obtain a family of VASS in dimension 3 whose shortest reachability witnessing runs are exponential, and we show that the reachability problem is NP-hard in dimension 7. These results resolve negatively questions that had been posed by the works of Blondin et al. in LICS 2015 and Englert et al. in LICS 2016, and contribute a first construction that distinguishes 3-dimensional flat VASS from 2-dimensional VASS. Our third result, by means of a novel family of products of integer fractions, shows that 4-dimensional VASS can have doubly exponentially long shortest reachability witnessing runs. The smallest dimension for which this was previously known is 14. Joint work with Wojciech Czerwinski, Slawomir Lasota, Ranko Lazic, Filip Mazowiecki. Paper available at https://arxiv.org/abs/2001.04327
mardi 24 mars 2020 Abhishek De (IRIF) A parallel syntax for non-wellfounded proof theory
Proof theory is the study of proofs as mathematical objects in their own right. Infinite proofs (eg. infinite descent proofs) are pervasive in mathematics. A formal way of characterizing such proofs can be done by looking at fixed point logics (eg. mu calculus) from proof-theoretic lenses. Baelde et. al. have proposed an infinitary sequent calculus (i.e. infinitely deep, finitely wide proofs) for linear logic with fixed points (muMALL). In this talk, following a brief history of proof theory and infinite proofs, I will introduce muMALL. However, the sequent calculus of muMALL turns out to be ``too sequential. In order to achieve more liberal cut elimination, we have devised infinets which are proofs nets (à la Curien) for the multiplicative fragment (muMLL). The later part of the talk will focus on infinets and ongoing work on these nets.
mardi 17 mars 2020 André Nies (University of Auckland ) Finite automata presentable groups
mardi 10 mars 2020 Florent Capelli (Université de Lille) An introduction to Knowledge compilation
Knowledge compilation aims to transform knowledge on a system, often
vendredi 28 février 2020 Howard Straubing (Boston College) Two Variable Logic with a Between Relation
It is well-known that every sentence of first-order logic over
mardi 18 février 2020 Janusz Schmude (MIMUW, University of Warsaw) An algebraic approach to equivalence of MSO transductions of graphs of bounded treewidth
We prove MSO-transductions of graphs of bounded treewidth have decidable
mardi 11 février 2020 Paul-Elliot Anglès Auriac (Institut Camille Jordan, Lyon) The reverse mathematics of Hindman's theorem
Reverse mathematics consists of the study of the minimal axioms needed to prove a theorem. A phenomenon that appeared at the beginning of this study is that among the natural theorems, an enormous majority are equivalent to one out of five axiomatic systems: the Big Five. The exceptions to this are mainly mainly theorems from combinatorics, the most famous being the Ramsey theorem for pairs. This makes combinatorics especially interesting in the context of reverse mathematics.
jeudi 06 février 2020 Maribel Fernandez (King's College London) Semantics and applications of PORGY - an interactive modelling framework based on strategic graph rewriting
In this talk I will describe the use of strategic port graph rewriting as a basis for the implementation of visual modelling tools. The goal is to facilitate the specification and analysis of complex systems. A system is represented by an initial graph and a collection of graph rewrite rules, together with a user-defined strategy to control the application of rules. The traditional operators found in strategy languages for term rewriting have been adapted to deal with the more general setting of graph rewriting, and some new constructs have been included in the strategy language to deal with graph traversal and management of rewriting positions in the graph. We give a formal semantics for the language, examples of application in the areas of biochemistry, social networks and database design, and a brief description of its implementation: the graph transformation and visualisation tool PORGY.
mardi 04 février 2020 Jérôme Leroux (CNRS, LaBRI) Reachability in fixed dimension vector addition systems with states
The reachability problem is a central decision problem for formal verification based on vector addition systems with states (VASS), which are equivalent to Petri nets and form one of the most studied and applied models of concurrency. Reachability for VASS is also inter-reducible with a plethora of problems from a number of areas of computer science. In spite of recent progress, the complexity of the reachability problem remains unsettled, and it is closely related to the lengths of shortest VASS runs that witness reachability.
mardi 28 janvier 2020 Sylvain Lombardy (LaBRI) A separation result on min-plus and max-plus automata
Work in collaboration with Thomas Colcombet.
mardi 21 janvier 2020 Denis Kuperberg (CNRS, ENS Lyon) Computational content of circular proof systems
Cyclic proofs are a class of formal proof systems that allow some kind of circular reasoning. Unlike classical proofs, represented by finite trees with axioms as leaves, cyclic proofs are represented by trees containing infinite branches. The Curry-Howard correspondence allows us to see these cyclic proofs as programs. We investigate the computational content of a cyclic proof system based on Kleene algebra, where we see expressions as data types. Different proofs of the same sequent e |- f can be interpreted as different programs mapping every input of type e to an output of type f. We show that depending on the particular rules allowed in the system, the computational content of proofs matches different known complexity classes: regular languages, LogSpace, primitive recursive functions, system T. Various tools are used to pinpoint these different expressive powers, including a newly introduced class of automata (Jumping Multihead Automata), and results from the field of reverse mathematics.
mardi 14 janvier 2020 Guillaume Lagarde (LaBRI) Lempel-Ziv: A one-bit catastrophe but not a tragedy
LZ'78 is a famous and very simple lossless data compression algorithm published by Abraham Lempel and Jacob Ziv in 1978. Although widely used in practise, we know little about its stability. The one-bit catastrophe question, introduced by Jack Lutz in the late 90s, asks whether an infinite word compressible by LZ'78 can become incompressible by adding a single bit in front of it. Our main result is to answer that question positively. We also give tight bounds on the maximal possible variation between the compression ratio of a finite word and its perturbation (when one bit is added in front of it), showing that to get a catastrophe, the initial word needs already to be close to the threshold of incompressibility.
mardi 07 janvier 2020 Raphaël Berthon (ULB) Mixing sure, almost sure, exist and probable objectives in MDPs
We consider algorithms to decide the existence of strategies in MDPs for Boolean combinations of objectives. These objectives are omega-regular properties that need to be enforced either surely (whatever happens), almost surely (with probability one), existentially (it can happen), or with non-zero probability. Such a combination of properties could be e.g. that an agent reaches a target with high probability while guaranteeing it will not crash. We provide algorithms to solve the general case of Boolean combinations and we also investigate relevant subcases. We provide algorithms to solve the general case of Boolean combinations and we also investigate relevant subcases. We also report on complexity lower-bounds for these problems.
mardi 17 décembre 2019 Mateusz Skomra (ENS Lyon) Using tropical geometry to obtain condition numbers of stochastic mean payoff games
In this talk, we introduce a condition number of stochastic mean payoff games. To do so, we interpret these games as feasibility problems over tropically convex cones. In this setting, the condition number is defined as the maximal radius of a ball in Hilbert's projective metric that is included in the (primal or dual) feasible set. We show that this conditioning controls the number of value iterations needed to decide whether a mean payoff game is winning. In particular, we obtain a pseudopolynomial bound for the complexity of value iteration provided that the number of random positions is fixed. We also discuss the implications of these results for convex optimization problems over nonarchimedean fields and present possible directions for future research.
mardi 10 décembre 2019 Edwin Hamel-De Le Court (Université de Rouen) Algebraic tools for state complexity
Computing the state complexity of regular operations is usually a messy business. Every new operation needs to be carefully considered and the associated computations need to be tweaked. We present an attempt to generalize this process on a large class of rational operations, and use this framework to present new results.
mardi 03 décembre 2019 Christine Tasson (IRIF, Paris 7) Semantics of Functional Probabilistic Programs
Probabilities are extensively used in Computer Science. Algorithms use probabilistic choices for solving problems that are untracktable deterministically or for improving efficiency. Recently, (Functional) Probabilistic Programming has been introduced for applications in Machine Learning and Artificial Intelligence. Probabilistic programs are used to describe statistical models and for developing probabilistic data analysis.
mardi 26 novembre 2019 Sebastian Junges (RWTH Aachen) Parameter Synthesis in Markov Models: An Overview
Markov models comprise states with probabilistic transitions..
mardi 19 novembre 2019 Nathanaël Fijalkow (CNRS, LaBRI) Learning probabilistic context-free grammars
In this talk I will present a solution to the following problem: given a set of strings, learn the underlying probabilistic context-free grammar generating these strings.
mardi 12 novembre 2019 Bartek Klin (MIMUW, University of Warsaw) Monadic monadic second order logic
Monadic second order logic (MSO) is usually studied over specific kinds of structures, be it finite words, infinite words, finite or infinite trees, total orders of various shapes, etc. A monad is a rather abstract notion of a kind of structures that covers these and many other examples. One can formulate an abstract definition of MSO for a generic monad. I will explain how this is done, and I will describe some conditions that a monad should satisfy to ensure a basic sanity check: that every definable language is recognized by a finite algebra.
mardi 05 novembre 2019 David Janin (LaBRI) An equational modeling of asynchronous concurrent programming
Asynchronous programing is a widely spread technique offering some simple concurrent programing primitives that are restricted enough so that the resulting concurrent programs are, to some extent, dead-lock free. In this talk, I shall present the notion of monadic references that allows for formally defining a model of asynchronous concurrent programming as an extension of the usual model of (say) sequential monad programing.
mardi 22 octobre 2019 Daniel Hausmann (Friedrich-Alexander University of Erlangen and Nürnberg) Computing Nested Fixpoints in Quasipolynomial Time
mardi 15 octobre 2019 Engel Lefaucheux (MPI SWS) Simple Priced Timed Games are not That Simple
mardi 08 octobre 2019 Guillaume Lagarde (LaBRI) Tradeoff between size and degree in Polynomial Calculus Resolution
Introduced by Cleggs et al. (STOC'96) to capture Gröbner basis computations, Polynomial Calculus Resolution (PCR) is an algebraic proof system for certifying the unsatisfiability of CNF formulas. Impagliazzo et al. (CC'99) established that if an unsatisfiable k-CNF formula over n variables has a refutation of small size in PCR (that is, polynomial size), then this formula also has a refutation of small degree, i.e., O(sqrt(n log n)). A natural question is to know whether we can achieve both small size and small degree in the same refutation.
mardi 01 octobre 2019 Hugo Gimbert (CNRS, LaBRI) Les algorithmes de Parcoursup
« Parcoursup » est la plateforme nationale d’admission en première année de l’enseignement supérieur, mise en place en 2018 suite au vote de la loi ORE, en remplacement d’APB (Admission Post-Bac). Cette plateforme assure la mise en relation des formations du supérieur (licences, BTS, IUT, écoles, prépas, etc…) avec les candidats à ces formations, près de 900.000 en 2019.
mardi 24 septembre 2019 Bruno Courcelle et Yves Métivier (LaBRI) Arbres infinis réguliers et revêtements universels de graphes finis
The notion of graph covering, from which we get that of a universal covering (an infinite tree) is important in the theory of distributed computing.
mardi 10 septembre 2019 Anantha Padmanabha (IMSC, Chennai) Two variable fragment of Term Modal logic
mardi 09 juillet 2019 Loïc Paulevé (CNRS, LaBRI) Most permissive semantics of Boolean networks
mardi 02 juillet 2019 Sreejith A V (IIT Goa) Block products for algebras over countable words
We look at words which are mappings from a countable linear ordering to a finite alphabet. Finite words, Omega words etc satisfy the above condition. In this talk, we study the languages (of words) definable by different logics. We consider monadic second order logic, first order logic, linear temporal logic etc.
mardi 25 juin 2019 Yann Strozecki (Université de Versailles Saint-Quentin) Solving Simple Stochastic Games with few RandomNodes faster using Bland’s Rule
A simple stochastic game, SSG for short, is a two-player zero-sum game, a turn-based version of stochastic games. SSGs were introduced by Condon and provide a general framework that allows to study algorithmic complexity issues underlying reachability objectives. The best algorithm so far for solving SSGs is Ludwig’s randomized algorithm which works in expected 2^O(sqrt(n)) time. We first give a simpler iterative variant of this algorithm, using Bland’s rule from the simplex algorithm, which uses exponentially less random bits than Ludwig’s version. Then, we show how to adapt this method to the algorithm of Gimbert and Horn whose worst case complexity is O(k!), where k is the number of random nodes. Our algorithm has an expected running time of 2^O(k) , and works for general random nodes with arbitrary outdegree and probability distribution on outgoing arcs.
mardi 18 juin 2019 Matthew Hague (University of London) Generic and Complete Algorithms for Straight-Line String Constraints
Path-feasibility is an important problem in the symbolic execution of
mardi 11 juin 2019 Anca Muscholl (LaBRI) The many facets of string transducers
The talk will be a survey on some recent results about string transducers.
mardi 04 juin 2019 Igor Walukiewicz (LaBRI) LambdaY-calculus with priorities
We will start with another view on alternating automata over finite
mardi 28 mai 2019 Karoliina Lehtinen (University of Liverpool) Parity, Buchi, Weak
This talk is about the trade-offs between different acceptance
mardi 21 mai 2019 Tobias Kappé (University College London) Kleene Algebras
mardi 14 mai 2019 Joanna Ochremiak (CNRS, LaBRI) On the power of symmetric linear programs
We consider families of symmetric linear programs (LPs) that decide a property of graphs in the sense that, for each size of graph, there is an LP defining a polyhedral lift that separates the integer points corresponding to graphs with the property from those corresponding to graphs without the property. We show that this is equivalent, with at most polynomial blow-up in size, to families of symmetric Boolean circuits with threshold gates. In particular, when we consider polynomial-size LPs, the model is equivalent to definability in a non-uniform version of fixed-point logic with counting. This is joint work with Albert Atserias and Anuj Dawar.
mardi 07 mai 2019 Charles Paperman (Université de Lille) Topological Sorting under Regular Constraints
In this talk, I will present a joint work with Antoine Amarilli, published at ICALP 18 about what we call the constrained topological sorting problem (CTS): given a regular language K and a directed acyclic graph G with labeled vertices, determine if G has a topological sort that forms a word in K.
mardi 30 avril 2019 Pierre Clairambault (CNRS, ENS Lyon) Linearity in Higher-Order Recursion Schemes
Higher-Order Model-Checking (HOMC) has recently emerged as an approach
mardi 16 avril 2019 Uri Zwick (Tel Aviv University) Faster k-SAT algorithms using biased-PPSZ
mardi 09 avril 2019 Donald Stull (Université de Lorraine, LORIA) Selection, Divergence, and Dichotomy
The Schnorr-Stimm dichotomy theorem concerns finite-state gamblers that bet on infinite sequences of symbols taken from a finite alphabet. The theorem asserts that, for each such sequence S, the following two things are true. 1. If S is normal in the sense of Borel (meaning that any two strings of equal length appear with equal asymptotic frequency in S), then every finite-state gambler loses money at an exponential rate betting on S. 2. If S is not normal, then there is a finite-state gambler that wins money at an exponential rate betting on S.
mardi 02 avril 2019 Sarah Winter (RWTH Aachen) Parameterized synthesis of sequential transducers from rational relations over finite words
The synthesis problem asks, given a specification that relates possible inputs to allowed outputs, whether there is a program realizing the specification, and if so, construct one.
mardi 26 mars 2019 Grégoire Sutre (LaBRI) Reachability for Two-Counter Machines with One Test and One Reset
We prove that the reachability relation of two-counter machines with one zero-test and one reset is Presburger-definable and effectively computable. Our proof is based on the introduction of two classes of Presburger-definable relations effectively stable by transitive closure. This approach generalizes and simplifies the existing different proofs and it solves an open problem introduced by Finkel and Sutre in 2000.
mardi 19 mars 2019 Vaishnavi Sundararajan (IRISA, Rennes) A theory of assertions for Dolev-Yao models
We undertake an abstract study of certification in security protocols, concentrating on the logical properties and derivability of certificates. Specifically, we extend the Dolev-Yao model with a new class of objects called ‘assertions’, along with an associated algebra for deriving new assertions from old ones. We also provide a case study via the FOO e-voting protocol, and provide algorithms for the derivability problem and the active intruder problem for this system.
mardi 12 mars 2019 Nathanaël Fijalkow (CNRS, LaBRI) The complexity of mean payoff games using universal graphs
We study the computational complexity of solving mean payoff games. This class of games can be seen as an extension of parity games, and they have similar complexity status: in both cases solving them is in NP and coNP and not known to be in P. In a breakthrough result Calude, Jain, Khoussainov, Li, and Stephan constructed in 2017 a quasipolynomial time algorithm for solving parity games, which was quickly followed by two other algorithms with the same complexity. Our objective is to investigate how these techniques can be extended to the study of mean payoff games. We construct two new algorithms for solving mean payoff games. Our first algorithm depends on the largest weight N (in absolute value) appearing in the graph and runs in sublinear time in N, improving over the previously known linear dependence in N . Our second algorithm runs in polynomial time for a fixed number k of weights.
mardi 05 mars 2019 Bruno Courcelle (LaBRI) Betweenness in order-theoretical trees
The ternary betweenness relation on a tree, B(x,y,z), indicates that y is on the unique path between x and z. This notion can be extended to order-theoretic trees defined as partial orders such that the set of nodes greater than any node is linearly ordered. In such generalized trees, the unique path between two nodes can have infinitely many nodes. We axiomatize in first-order or monadic second-order logic several betweenness relations in order-theoretical trees.
mardi 12 février 2019 Marc Noy (Universitat Politècnica de Catalunya) Logic and random graphs
We look at properties of graphs that can be expressed in first order (FO) logic. Given such a property A and a class G of random graphs, we are interested in the limiting probability that a graph in G satisfies A, when the number of vertices goes to infinity.
lundi 11 février 2019 Paul-Elliot Angles d'Auriac (Institut Camille Jordan, Lyon) TBA
mardi 05 février 2019 Nathan Grosshans (ENS Paris) The power of programs over monoids taken from some small varieties of finite monoids
The computational model of programs over monoids, introduced by Barrington and Thérien in the late 1980s, gives a way to generalise the notion of (classical) recognition through morphisms into monoids in such a way that almost all open questions about the internal structure of the complexity class NC^1 can be reformulated as understanding what languages (and, in fact, even regular languages) can be program-recognised by monoids taken from some given variety of finite monoids. Unfortunately, for the moment, this finite semigroup theoretical approach did not help to prove any new result about the internal structure of NC^1 and, even worse, any attempt to reprove well-known results about this internal structure (like the fact that the language of words over the binary alphabet containing a number of 1s not divisible by some fixed integer greater than 1 is not in AC^0) using techniques stemming from algebraic automata theory failed.
mardi 29 janvier 2019 Meghyn Bienvenu (LaBRI) Ontology-Mediated Query Answering with OWL 2 QL Ontologies: Combined Complexity and Succinctness of Rewritings
The problem of ontology-mediated query answering (OMQA) has gained significant interest in recent years. One popular ontology language for OMQA is OWL 2 QL, a W3C standardized language based upon the DL-Lite description logic. This language has the desirable property that OMQA can be reduced to database query evaluation by means of query rewriting. In this talk, I will consider two fundamental questions about OMQA with OWL 2 QL ontologies: 1) How does the worst-case complexity of OMQA vary depending on the structure of the ontology-mediated query (OMQ)? In particular, under what conditions can we guarantee tractable query answering? 2) Is it possible to devise query rewriting algorithms that produce polynomial-size rewritings? More generally, how does the succinctness of rewritings depend on OMQ structure and the chosen format of the rewritings?
mardi 22 janvier 2019 Vincent Penelle (LaBRI) On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems
Karp and Miller's algorithm is a well-known decision procedure that solves the termination and boundedness problems for vector addition systems with states (VASS), or equivalently Petri nets. This procedure was later extended to a general class of models, well-structured transition systems, and, more recently, to pushdown VASS. In this paper, we extend pushdown VASS to higher-order pushdown VASS (called HOPVASS), and we investigate whether an approach à la Karp and Miller can still be used to solve termination and boundedness.
mardi 15 janvier 2019 Marie van den Bogaard (Université Libre de Bruxelles) Beyond admissibility: Dominance between chains of strategies
In this talk, we focus on the concept of rational behaviour in multi-player games on finite graphs, taking the point of view of a player that has access to the structure of the game but cannot make assumptions on the preferences of the other players. In the qualitative setting, admissible strategies have been shown to fit the rationality requirements, as they coincide with winning strategies when these exist, and enjoy the fundamental property that every strategy is either admissible or dominated by an admissible strategy. However, as soon as there are three or more payoffs, one finds that this fundamental property does not necessarily hold anymore: one may observe chains of strategies that are ordered by dominance and such that no admissible strategy dominates any of them. Thus, to recover a satisfactory rationality notion (still based on dominance), we depart from the single strategy analysis approach and consider instead chains of strategies as families of behaviours. We establish a sufficient criterion for games to enjoy a similar fundamental property, ie, all chains are below some maximal chain, and, as an illustration, we present a class of games where admissibility fails to capture some intuitively rational behaviours, while our chain-based analysis does. Based on a joint work with N.Basset, I. Jecker, A. Pauly and J.-F. Raskin, presented at CSL'18.
mardi 08 janvier 2019 Gabriele Puppis (LaBRI) Unambiguous Register Automata
In the literature we find many computation models whose expressiveness goes beyond finite automata, however without attaining the full power of Turing machines. The common practice is to enrich finite automata with some internal memory (e.g. counters, clocks, stacks, etc.) that can be used to store, manipulate, and compare data from a potentially infinite domain. An intriguing model that results from this practice is the model of register automaton, which is essentially a finite automaton equipped with a finite number of registers. Register automata are used to recognize languages over infinite alphabets. The deterministic, unambiguous, and non-deterministic variants of these automata form a hierarchy of strictly increasing expressive power, where the bottom and top levels have, respectively, decidable and undecidable equivalence problems. Accordingly, the intermediate class of unambiguous register automata is an interesting object of study, since it is believed to be robust and algorithmically well-behaved.
mardi 18 décembre 2018 David Carral (TU Dresden) Reasoning over Existential Rules with Acyclicity Notions
The chase is a sound and complete (albeit non-terminating) algorithm for conjunctive query answering over ontologies of existential rules. On the theoretical side, we develop sufficient conditions to guarantee its termination (i.e., acyclicity notions), and study several restrictions that furthermore ensure its polynomiality. On the practical side, we empirically study the generality of these conditions and we extend the Datalog engine VLog to develop an efficient implementation of the chase. Furthermore, we conduct an extensive evaluation, and show that VLog can compete with the state of the art, regarding runtime, scalability, and memory efficiency.
mardi 11 décembre 2018 Filip Mazowiecki (LaBRI) When are Emptiness and Containment Decidable for Probabilistic Automata?
The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata. It is well known that both problems are undecidable. In this paper we provide a more refined view of these problems in terms of the degree of ambiguity of probabilistic automata. We show that a gap version of the emptiness problem (that is known be undecidable in general) becomes decidable for automata of polynomial ambiguity. We complement this positive result by showing that the emptiness problem remains undecidable even when restricted to automata of linear ambiguity. We then turn to finitely ambiguous automata. Here we show decidability of containment in case one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Our proof of this last result relies on the decidability of the theory of real exponentiation, which has been shown, subject to Schanuel's Conjecture, by Macintyre and Wilkie.
mardi 04 décembre 2018 Nathanaël Fijalkow (LaBRI) Data generation for programme synthesis
Programming by example is the problem of synthesising a program from a small set of pairs input and output. Despite having found applications in several areas it is notoriously computationally expensive. Recent works have considered hybrid approaches combining ML and PL based techniques. These techniques require generating a training dataset, which leads to significant difficulties related to finding the most informative inputs to characterise a given programme.
mardi 20 novembre 2018 Laurent Bienvenu (LaBRI) Optimal bounds for single-source Kolmogorov extractors
The rate of randomness (or dimension) of a binary string x is the ratio C(x)/|x| where C(x) is the Kolmogorov complexity of x. While it is known that a single computable transformation cannot increase the rate of randomness of all strings, Fortnow et al. showed that for any 0
mardi 13 novembre 2018 Sylvain Schmitz (LSV, ENS Cachan) Complexity bounds for bisimulation equivalence in first-order grammars
Following Géraud Sénizergues' seminal results twenty years ago on the decidability of language equivalence of deterministic pushdown automata and of (weak) bisimilation equivalence of (epsilon-popping) pushshdown automata, several works have attempted to provide complexity bounds for these problems. For instance, some significant simplifications over the original proofs were provided by Colin Stirling and Petr Jancar, using in particular the formalism of first-order grammars instead of pushdown automata, and resulting in Tower upper bounds for the language equivalence problem in deterministic systems. But no complexity bounds were known for the bisimulation equivalence problem.
mardi 06 novembre 2018 Jérôme Leroux (LaBRI) The Reachability Problem for Petri Nets is Not Elementary
Petri nets, also known as vector addition systems, are a long established and widely used model of concurrent processes. The complexity of their reachability problem is one of the most prominent open questions in the theory of verification. That the reachability problem is decidable was established by Mayr in his seminal STOC 1981 work, and the currently best upper bound is non-primitive recursive cubic-Ackermannian of Leroux and Schmitz from LICS 2015. We show that the reachability problem is not elementary. Until this work, the best lower bound has been exponential space, due to Lipton in 1976.
mardi 23 octobre 2018 Cristian Riveros (Pontificia Universidad Catolica de Chile) Foundations of Complex Event Processing
Complex event processing (CEP) emerges as a unified technology for efficiently processing data streams. Contrary to data streams management systems, CEP query languages model data streams as a continuous sequence of events and CEP queries define sets of events (complex events) that are of interest for the final user.
mardi 09 octobre 2018 Marie Fortin (LSV, ENS Cachan) It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with Happened Before
Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which finite-state processes exchange messages through unbounded FIFO channels. We study the first-order logic of MSCs, featuring Lamport's happened-before relation. We introduce a star-free version of propositional dynamic logic (PDL) with loop and converse. Our main results state that (i) every first-order sentence can be transformed into an equivalent star-free PDL sentence (and conversely), and (ii) every star-free PDL sentence can be translated into an equivalent CFM. This answers an open question and settles the exact relation between CFMs and fragments of monadic second-order logic. As a byproduct, we show that first-order logic over MSCs has the three-variable property.
mardi 02 octobre 2018 A. V. Sreejith (IIT Goa) Languages over countable linear orderings
We look at words which are mappings from a countable linear ordering to a finite alphabet. Finite words, Omega words etc satisfy the above condition. We will also look at other kind of words.
mardi 25 septembre 2018 María Emilia Descotte (LaBRI) Closure properties of synchronized relations
A standard approach to define k-ary word relations over a finite alphabet A is through k-tape finite state automata that recognize regular languages L over {1, ... , k} x A, where (i,a) is interpreted as reading letter a from tape i. Accordingly, a word w in L denotes the tuple (u_1, ... , u_k) of words over A in which u_i is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of Rational relations, enforcing restrictions on the reading regime from the tapes, which we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language L onto {1, ... , k}. In this way, for each regular language C over the alphabet {1, ... , k}, one obtains a class Rel(C) of relations. Synchronous, Recognizable, and Length-preserving rational relations are all examples of classes that can be defined in this way.
mardi 03 juillet 2018 Filip Murlak (University of Warsaw) Ontology-mediated query answering for expressive description logics, or yet another family of (potentially) decidable fragments of first-order logic
Evaluating queries in the presence of background knowledge has been extensively studied in several communities. In database theory, it is known as query answering under integrity constraints: given a finite database instance and a set of constraints, determine answers to a query that are certain to hold over any extension of the given instance that satisfies the constraints. In the knowledge representation community, the database instance and the set of constraints are treated as a single object, called an ontology, but otherwise the problem remains the same, except that different kinds of constraints are interesting. While in database theory constraints are usually very simple, like functionality of relations, or inclusions between relations, in knowledge representation more expressive logics are used. I will focus on so called description logics, which are a family of extensions of modal logic. I will cover some basic techniques, a highly non-trivial result by Rudolph and Glimm (2010), as well as some recent results obtained with Tomek Gogacz (U Warsaw) and Yazmin Ibanez-Garcia (TU Wien).
mardi 26 juin 2018 Sébastien Labbé (LaBRI) On Jeandel-Rao aperiodic tilings
In 2015, Jeandel and Rao showed by exhaustive computer search that every Wang tile set of cardinality
mardi 19 juin 2018 František Blahoudek (Masaryk University) Semi-deterministic automata: How to obtain and complement them
Semi-deterministic Büchi automata (sDBA) are useful for example in model checking of probabilistic systems or in termination analysis. While in probabilistic model checking sDBA represent the set of behaviours of interest, in termination analysis they represent terminating behaviours of programs and are often complemented to perform a language difference. In my talk, I first introduce the class of semi-deterministic Büchi automata (sDBA). Then I will explain how can we convert nondeterministic Büchi automata (NBA) into sDBA, followed by a discussion on how to efficiently convert generalized Büchi automata into sDBA. After we learn how to build sDBA, I will introduce a complementation algorithm sDBA. The algorithm produces a complement automata with at most 4^n states while the best upper bound on complementation of NBA is O((0.76n)^n). Further, our algorithm produces automata with a very low degree of nondeterminism, indeed, the resulting automata are even unambiguous.
mardi 12 juin 2018 Bruno Guillon (University of Milan) Undecidability of MSO+“ultimately periodic”
We prove that MSO on omega-words becomes undecidable if allowing to quantify over sets of positions that are ultimately periodic, i.e., sets X such that for some positive integer p, ultimately either both or none of positions x and x+p belong to X. We obtain it as a corollary of the undecidability of MSO on omega-words extended with the second-order predicate U1(X) which says that the distance between consecutive positions in a set X of naturals is unbounded. This is achieved by showing that adding U1 to MSO gives a logic with the same expressive power as MSO+U, a logic on omega-words with undecidable satisfiability.
mardi 05 juin 2018 Laure Daviaud (University of Warwick) A pseudo-quasi-polynomial algorithm for mean-payoff parity games
In a mean-payoff parity game, one of the two players aims both to achieve a qualitative parity objective and to minimize a quantitative long-term average of payoffs (aka. mean payoff). The game is zerosum and hence the aim of the other player is to either foil the parity objective or to maximize the mean payoff.
mardi 22 mai 2018 K. Narayan Kumar (Chennai Mathematical Institute) Verification of Asynchronous Programs with Nested Locks
We consider asynchronous programs consisting of multiple recursive threads (modeled as pushdown systems) running in parallel. Each of the threads is equipped with a multi-set. The threads can create tasks and post them onto the multi-sets or read a task from their own. In addition, they can synchronize through a finite set of locks. We examine the decidability of the state reachability problem for this model. The problem is already known to be undecidable for a system consisting of two recursive threads (and no tasks) and we examine a decidable subclass.
mardi 15 mai 2018 Madhavan Mukund (Chennai Mathematical Institut) Modelling replicated data stores with multiple correctness levels
Replicated data stores typically sacrifice strong consistency guarantees in favour of availability and partition tolerance. These data stores usually provide specific weaker consistency guarantees, such as eventual consistency, monotonic reads or causal consistency.
mardi 24 avril 2018 Armin Weiß (Stuttgart University) The isomorphism problem for virtually free group
Since Muller and Schupp's result it is well-known that the finitely generated virtually free groups are precisely the context-free groups. The isomorphism problem for virtually free groups, has shown to be decidable by Kristic. In the special case that the input groups are either given as context-free grammars for their word problems or as so-called virtually free presentations, it is primitive recursive by the work of Sénizergues.
mardi 17 avril 2018 Pierre Ohlmann (IRIF, Paris 7) Arithmetic circuits as automata, and applications
We give a syntactic correspondence between non-associative arithmetic circuits and acyclic weighted tree automata. We may then export results from automata theory to non-associative circuits and characterize the size of a minimal circuit for a given polynomial as the rank of a Hankel matrix. We will then show how this can be used to re-obtain Nisan's theorem on Algebraic Branching Programs as well as recent results on Unique Parse Tree circuits. Lastly, we will highlight a new way of obtaining lower bounds for general (associative) arithmetic circuits.
mardi 10 avril 2018 Nathanaël Fijalkow (LaBRI) The State Complexity of Alternating Automata
We study the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. We look at alternating automata as introduced by Chandra, Kozen and Stockmeyer: such machines run independent computations on the word and gather their answers through boolean combinations.
mardi 03 avril 2018 Louis-Marie Dando (LaBRI) On Rotating Q-Automata
I present results on rotating Q-automata, which are (memoryless) automata with weights in Q that can read the input tape from left to right several times. We show that the series realized by valid rotating Q-automata are Q-Hadamard series (which are the closure of Q-rational series by pointwise inverse), and that every Q-Hadamard series can be realized by such an automaton. We prove that, although validity of rotating Q-automata is undecidable, the equivalence problem is decidable on rotating Q-automata. Finally, we prove that every valid two-way Q -automaton admits an equivalent rotating Q-automaton. The conversion, which is effective, implies the decidability of equivalence of two-way Q-automata.
mardi 27 mars 2018 Valia Mitsou (Université Paris Diderot, IRIF) Limitations of treewidth for problems beyond NP.
***Joint seminar with Graphes et Optimisation***
mardi 20 mars 2018 Dominik Velan (Masaryk University) Asymptotic Bounds on Termination Time in VASS
Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parametrized systems, and are also used as abstract models of programs in resource bound analysis. We study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. First, I will present a characterization for VASS with linear asymptotic complexity. I will also show that if a complexity of a VASS is not linear, it is at least quadratic.
mardi 13 mars 2018 Jérôme Leroux (LaBRI) Polynomial Vector Addition Systems With States
The reachability problem for vector addition systems is one of the most difficult and central problem in theoretical computer science. The problem is known to be decidable, but despite instance investigations during the last four decades, the exact complexity is still open. For some sub-classes, the complexity of the reachability problem is known. Structurally bounded vector addition systems, the class of vector addition systems with finite reachability sets from any initial configuration, is one of those classes. In fact, the reachability problem was shown to be polynomial-space complete for that class by Praveen and Lodaya in 2008. Surprisingly, extending this property to vector addition systems with states is open. In fact, there exist vector addition systems with states that are structurally bounded but with Ackermannian large sets of reachable configurations. It follows that the reachability problem for that class is between exponential space and Ackermannian. In this paper we introduce the class of polynomial vector addition systems with states, defined as the class of vector addition systems with states with size of reachable configurations bounded polynomially in the size of the initial ones. We prove that the reachability problem for polynomial vector addition systems is exponential-space complete. Additionally, we show that we can decide in polynomial time if a vector addition system with states is polynomial. This characterization introduces the notion of iteration scheme with potential applications to the reachability problem for general vector addition systems.
mardi 06 mars 2018 Pierre Casteran (LaBRI) The hydra and the rooster
The Hydra game was introduced in 1982 by the mathematicians L. Kirby and J. Paris in their article: Accessible Independence Results for Peano Arithmetic.
mardi 27 février 2018 María Emilia Descotte (LaBRI) Resynchronizing Classes of Word Relations
A natural approach to defining binary word relations over a finite alphabet A is through two-tape finite state automata, which can be seen as regular languages L over the alphabet {1,2}xA, where (i,a) is interpreted as reading letter a from tape i. Thus, a word w of the language L denotes the pair (u_1,u_2) in A* x A* in which u_i is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of Rational relations (a.k.a. non-deterministic finite state transducers), enforcing restrictions on the reading regime from the tapes, that we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language onto {1,2}. In this way, for each regular language C contained in {1,2}*, one obtains a class Rel(C) of relations, such as the classes of Regular, Recognizable, or length-preserving relations, as well as (infinitely) many other classes.
mardi 13 février 2018 Michael Raskin (LaBRI) Complementing the languages of unambigous automata
Unambiguous non-deterministic finite automata have intermediate
mardi 06 février 2018 Lukas Fleischer (Stuttgart University) The Complexity of Decision Problems for Recognizing Morphisms
We discuss the complexity of decision problems on regular languages represented by morphisms to finite semigroups. There are two canonical ways of specifying the semigroup: giving its multiplication table or an implicit description as the subsemigroup of a transformation semigroup (generated by the images of the given morphism). For both representations, we will consider
mardi 30 janvier 2018 David Janin (LaBRI) Animation 3D et produit semi-direct
We define a simple and sound mathematical framework for describing temporal media programming language semantics based on the various concepts offered by semigroup theory. As a result a fairly general programming scheme can be defined in order to specify, compose and render both spatial media objects (e.g. 3D drawings) and timed media objects (e.g. Animation or Music). As an example, a simple monoid based semantics model of the turtle command language of Logo is detailed and extended throughout.
mardi 23 janvier 2018 Filip Mazowiecki (LaBRI) Pumping lemmas for weighted automata
We present three pumping lemmas for three classes of functions definable by fragments of weighted automata over the min-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus semiring.
mardi 09 janvier 2018 Philippe Duchon (LaBRI) Simulabilité à mémoire finie de lois de probabilités continues
On s'intéresse à la question de la simulation exacte de lois de probabilités continues sur les réels, et plus précisément, à identifier quelles lois sont simulables exactement en n'utilisant qu'une mémoire finie - le modèle naturel étant une variante d'automates probabilistes, mais il est facile de voir que divers modèles sont équivalents (au moins au sens probabiliste de presque sûrement).
mardi 12 décembre 2017 Cyril Gavoille (LaBRI) La coloration de graphe dans le modèle LOCAL - Partie II
Partie II:
mardi 05 décembre 2017 Cyril Gavoille (LaBRI) La coloration de graphe dans le modèle LOCAL - Partie I
L'objectif de cette série d'exposés est de faire découvrir un résultat aussi élégant que surprenant du calcul distribué, à savoir la 3-coloration des n-cycles en temps log*(n). On démontrera l'optimalité de ce résultat ainsi que ces généralisations au cas des graphes arbitraires.
mardi 28 novembre 2017 Ranko Lazic (Warwick University) Succinct progress measures and solving parity games in quasi-polynomial time
The recent breakthrough paper by Calude et al. (a winner of STOC 2017 Best Paper Award) has given the first algorithm for solving parity games in quasi-polynomial time, where previously the best algorithms were mildly sub-exponential. We devise an alternative quasi-polynomial time algorithm based on progress measures, which allows us to reduce the space required from quasi-polynomial to nearly linear. Our key technical tools are a novel concept of ordered tree coding, and a succinct tree coding result that we prove using bounded adaptive multi-counters, both of which are interesting in their own right.
mardi 21 novembre 2017 Angelo Montanari (University of Udine) Model Checking: the Interval Way
Model checking with interval temporal logics is emerging as a viable alternative to model checking with standard point-based temporal logics, such as LTL, CTL, CTL*, and the like. The behavior of the system is modelled by means of (finite) Kripke structures, as usual. However, while temporal logics which are interpreted point-wise describe how the system evolves state-by-state, and predicate properties of system states, those which are interpreted interval-wise express properties of computation stretches, spanning a sequence of states. A proposition letter is assumed to hold over a computation stretch (interval) if and only if it holds over each component state (homogeneity assumption). The most well-known interval temporal logic is Halpern and Shoham's modal logic of time intervals HS, which features one modality for each possible ordering relation between a pair of intervals, apart from equality. In the seminar, we provide an overview of the main results on model checking with HS and its fragments under the homogeneity assumption. In particular, we show that the problem turns out to be non-elementarily decidable and EXPSPACE-hard for full HS, but it is often computationally much better for its fragments. Then, we briefly compare the expressiveness of HS in model checking with that of LTL, CTL, CTL*. We conclude by discussing a recent generalization of the proposed MC framework that allows one to use regular expressions to define the behavior of proposition letters over intervals in terms of the component states.
mardi 14 novembre 2017 MF (LaBRI) Reunion d'equipe MF
mardi 07 novembre 2017 Loïc Paulevé (LRI - Paris Sud) Formal methods for capturing dynamics of biological networks
Computational models of biological networks aim at reporting the indirect influences between the different molecular entities acting within the cell (genes, RNA, proteins, ...). In this talk, I will give an overview of methods for the formal assessment of dynamics of biological networks by static analysis. After an introduction to Boolean networks and their relevance for modelling cell signalling and gene regulatory networks, I'll present an abstract interpretation of their trajectories based on a causal analysis. Then, I'll show how we can combine this abstraction with SAT approches to address systems biology challenges, such as model identification and cell reprogramming.
mardi 31 octobre 2017 Vincent Penelle (LaBRI) Rewriting Higher-order Stack Trees
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the satisfaction of any formula written in monadic second order logic (respectively first order logic with reachability predicates) can be decided on such a graph.
mardi 24 octobre 2017 Amina Doumane (LIP - ENS Lyon) Constructive completeness for the linear-time mu-calculus
Modal mu-calculus is one of the central logics for verification. In his seminal paper, Kozen proposed an axiomatization for this logic, which was proved to be complete, 13 years later, by Kaivola for the linear-time case and by Walukiewicz for the branching-time one. These proofs are based on complex, non-constructive arguments, yielding no reasonable algorithm to construct proofs for valid formulas. The problematic of constructiveness becomes central when we consider proofs as certificates, supporting the answers of verification tools. We provide a new completeness argument for the linear-time mu-calculus which is constructive, i.e. it builds a proof for every valid formula. To achieve this, we decompose this difficult problem into several easier ones, taking advantage of the correspondence between the mu-calculus and automata theory. More precisely, we lift the well-known automata transformations (non-determinization for instance) to the logical level. To solve each of these smaller problems, we perform first a proof-search in a circular proof system, then we transform the obtained circular proofs into proofs in Kozen's axiomatization. This yields a constructive proof for the full linear-time mu-calculus.
mardi 17 octobre 2017 David Janin (LaBRI) Timed domains: an appetizer
we develop a general theory of timed domains and timed morphisms that aims at offering a versatile and sound mathematical framework for the study of timed denotational semantics of networks of timed programs. The proposed compositional semantic model accounts for the fact that every non trivial computation step necessarily takes some non zero time. This is achieved by defining timed domains as classical domains (directed complete posets) where time appears everywhere: every increase of knowledge necessarily refers to the passage of time. Timed morphisms are defined as functions between timed domains which uniformly act on the underlying time scales. The resulting category is a (bi)cartesian closed category with (mostly) internal henceforth timed least fixpoint operators. Moreover, by allowing (almost) arbitrary posets as time scales, the proposed frame- work also covers typical features of parallel or concurrency theory such as parallel, indenpendant or conflicting computations. In other words, timed domains and timed morphisms provide a fully featured mathematical framework for the study of computable spatio-temporal functions.
mardi 10 octobre 2017 Miguel Romero (Oxford University) The complexity of graph query languages
A graph database is a directed graph where each edge is additionally labeled with a symbol from a finite alphabet. Several data models, such as the ones occurring in the Semantic Web or semi-structured data, can be naturally captured via graph databases. In this context, one is not only interested in traditional queries, such as conjunctive queries, but also in navigational queries that take the topology of the data into account.
mardi 03 octobre 2017 Joanna Ochremiak (IRIF) Proof complexity of constraint satisfaction problems
Many natural computational problems, such as satisfiability and systems of equations, can be expressed in a unified way as constraint satisfaction problems (CSPs). In this talk I will show that the usual reductions preserving the complexity of the constraint satisfaction problem preserve also its proof complexity. As an application, I will present two gap theorems, which say that CSPs that admit small size refutations in some classical proof systems are exactly the constraint satisfaction problems which can be solved by Datalog.
mardi 26 septembre 2017 Vincent Penelle (LaBRI) Which classes of origin graph are generated by transducers?
This talk is about transductions, which are binary relations on words. We are interested in various models computing transductions (ie, transducers), namely two-way automata with outputs, streaming string transducers and string-to-string MSO transductions. We observe that each of these formalisms provides more than just a set of pairs of words. Indeed, one can also reconstruct origin information, which says how positions of the output string originate from positions of the input string. On the other hand, it is also possible to provide any pair of words in a relation with an origin mapping, indicating an origin input position for each output position, in a similar way. This defines a general object called origin graph. We first show that the origin semantic is natural and corresponds to the intuition we have of the run of a transducer, and is stable from translation from one model to another. We then characterise the families of origin graphs which corresponds to the semantics of streaming string transducers.
mardi 04 juillet 2017 Stefan GRUNER (University of Pretoria, South Africa) SAT-based Bounded Model Checking for 3-Valued Abstractions - Part II
Continuation of his precedent talk.
mardi 27 juin 2017 Stefan GRUNER (University of Pretoria, South Africa) SAT-based Bounded Model Checking for 3-Valued Abstractions
In this talk I will present joint work with Nils Timm (and students) from the University of Pretoria on how to make model-checking of concurrent systems more effective and more efficient. In the first part of the talk, which is based on our SBMF'16 paper, I show how bounded model-checking over a three-valued truth domain {T:true, F:false, U:unknown} can be translated into a classical Boolean satisfiability problem which can then be given to any classical SAT solver. In the second part of the talk, which is based on our recent FSEN'17 paper, I speak about efficiency-increasing heuristics which are based on the availability of structural knowledge about the original system to be model-checked. On the basis of such structural knowledge the SAT solver can be guided into 'promising' search paths, whereby the probability of unnecessarily exploring fruitless paths is considerably diminished. The SBMF'16 paper was acknowledged as the 2nd-best paper of the conference, and the FSEN'17 paper was nominated among the top three papers of the conference.
mardi 13 juin 2017 Emilia Descotte (UBA, Argentine) Axiomatizations for downward XPath on Data Trees
We give sound and complete axiomatizations for XPath with data tests by equality or inequality, and containing the single child axis. This data-aware logic predicts over data trees, which are tree-like structures whose every node contains a label from a finite alphabet and a data value from an infinite domain. The language allows us to compare data values of two nodes but cannot access the data values themselves (i.e., there is no comparison by constants).
mardi 30 mai 2017 Victor Marsault (University of Liège) An efficient algorithm to decide the periodicity of b-recognisable sets using MSDF convention
Given an integer base b
mardi 23 mai 2017 Michael Raskin (LaBRI) A linear lower bound for incrementing a space-optimal integer representation in the bit-probe model
We present the first linear lower bound for the number of bits required to be accessed in the worst case to increment an integer in an arbitrary space-optimal binary representation. The best previously known lower bound was logarithmic. It is known that a logarithmic number of read bits in the worst case is enough to increment some of the integer representations that use one bit of redundancy, therefore we show an exponential gap between space-optimal and redundant counters.
mardi 16 mai 2017 Igor Walukiewicz (LaBRI) Proving safety of concurrent programs
This talk will be based on the paper from POPL 2017:
mardi 09 mai 2017 Alain Finkel (LSV, ENS Cachan) WBTS: the new class of WSTS without WQO.
We present the ideal framework [FG09a,BFM14] which was recently used to obtain new deep results on Petri nets and extensions. If time, we will present the proof of the famous but unknown Erdös-Tarski theorem. We argue that the theory of ideals prompts a renewal of the theory of WSTS by providing a way to define a new class of monotonic systems, the so-called Well Behaved Transition Systems, which properly contains WSTS, and for which coverability is still decidable by a forward algorithm.
mardi 25 avril 2017 Nathan Lhote (LaBRI) On Reversible Transducers
Deterministic two-way transducers define the robust class of regular functions which is, among other good properties, closed under composition.
mardi 04 avril 2017 Andrzej Murawski (University of Warwick) Automata theory and game semantics of higher-order computation
I will give a survey of various classes of automata that have
mardi 28 mars 2017 David Janin (LaBRI) Time domain (for time denotational semantics)
Directed complete partial orders (cpos) are used in denotational semantics for describing the way each value is incrementally computed, passing from a completely unknown value to a completely known value. Then, continuous functions between cpos propagate increase of knowledge on their inputs to increase of knowledge on their outputs.
mardi 21 mars 2017 Laurent Bienvenu (LIRMM Montpellier) Learning probability measures
Suppose we have a probabilistic algorithm given as a black box and we have access to an output of this algorithm. There are two - related - questions one could ask. (1) Is it possible to make a plausible guess as to which algorithm is in the box? (2) Can we use the output of this algorithm as a random number generator by extracting `pure’ randomness from it? We will look at these questions from the point of view of computability and algorithmic learning theory. [Based on joint work with S. Figueira, B. Monin, and A. Shen]
mardi 14 mars 2017 Gabriele Puppis (LaBRI) On the decomposition of finite-valued streaming string transducers
I will present some preliminary results towards a proof of a decomposition theorem for streaming string transducers (SSTs). Roughly, the conjectured decomposition theorem states that every SST that associates at most k outputs to each input can be effectively decomposed as a finite union of functional SSTs. Such a result would imply, among other things, the decidability of the equivalence problem for the considered class of transducers as well as a correspondence with the classical two-way transducers. I will present a proof of this decomposition theorem in the special case of SSTs with 1 register. The proof heavily relies on a combinatorial result by Kortelainen concerning word equations with iterated factors.
mardi 07 mars 2017 Charles Grellois (University of Bologna) Verifying properties of functional programs: from the deterministic to the probabilistic case
In functional programs, also called higher-order programs, functions may take functions themselves as arguments. As a result, their model-checking relies in most approaches on semantic or type-theoretic tools. In this talk, I will explain how an analysis based on linear logic of a model-checking result of 2009 by Kobayashi and Ong led Melliès and I to the construction of a model for model-checking. This model is such that, when interpreting a term with recursion representing the tree of traces of a functional program, its denotation determines whether it satisfies a MSO property of interest. A related and similar model was obtained independently by Salvati and Walukiewicz.
mardi 28 février 2017 Emmanuel Fleury (LaBRI) Digital Currencies
Electronic money is a quite old problem in cryptology (Chaum, 1982) but recent discoveries lead to the birth of a new type of digital currency such as Bitcoins or Ethereum. Most of the new crypto-currencies are based on the concept of Blockchain which is used to maintain a trusted consensus in a distributed manner thanks to cryptographic primitives.
mardi 14 février 2017 Hugo Gimbert (LaBRI) Emptiness of nonzero automata is decidable
Zero automata are a probabilistic extension of parity automata on infinite trees.
mardi 24 janvier 2017 Rasmus Ibsen-Jensen (IST Austria) Faster algorithms for program analysis
The talk is based on joint work with Krishnendu Chatterjee, Amir Kafshdar Goharshady, Prateesh Goyal, and Andreas Pavlogiannis.
mardi 10 janvier 2017 B Srivathsan (CMI Chennai) Why liveness for timed automata is hard, and what we can do about it
The liveness problem for timed automata asks if a given automaton has an infinite run visiting an accepting state infinitely often. In this talk, we will show that if P is not equal to NP, the liveness problem is more difficult than the reachability problem - more precisely, we will exhibit a family of automata for which reachability is in P whereas liveness is NP-hard. We will then present a new algorithm to solve the liveness problem, and compare it with existing solutions.