Wednesday at 2pm, room 4033
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The goal of this reading group is to present in two hours blackboard sessions for some classical or more recent results concerning logic, automata theory, algebraic methods and games.
The reading group happens the Wednesday from 2pm to 4pm, room 4033, building Sophie Germain, every two weeks on average.
Logic, automata, algebra and games
Wednesday May 22, 2019, 2:15PM, 3052
Uri Zwick (Blavatnik School of Computer Science) Games on Graphs and Linear Programming Abstractions, Part 7/7: Lower bounds for Random-Facet and Random-Edge
https://www.irif.fr/_media/actualites/ressources/zwick_program.pdf
Logic, automata, algebra and games
Wednesday May 15, 2019, 2:15PM, 3052
Uri Zwick (Blavatnik School of Computer Science) Games on Graphs and Linear Programming Abstractions, Part 6/7: Lower bounds for Policy Iteration
https://www.irif.fr/_media/actualites/ressources/zwick_program.pdf
Logic, automata, algebra and games
Wednesday April 17, 2019, 2:15PM, 3052
Uri Zwick (Blavatnik School of Computer Science) Games on Graphs and Linear Programming Abstractions, Part 5/7: Parity Games
https://www.irif.fr/_media/actualites/ressources/zwick_program.pdf
Logic, automata, algebra and games
Wednesday April 10, 2019, 2:15PM, 3052
Uri Zwick (Blavatnik School of Computer Science) Games on Graphs and Linear Programming Abstractions, Part 4/7: Acyclic Unique Sink Orientations (AUSOs)
https://www.irif.fr/_media/actualites/ressources/zwick_program.pdf
Logic, automata, algebra and games
Wednesday April 3, 2019, 2:15PM, 3052
Uri Zwick (Blavatnik School of Computer Science) Games on Graphs and Linear Programming Abstractions, Part 3/7: Randomized sub-exponential time algorithm
https://www.irif.fr/_media/actualites/ressources/zwick_program.pdf
Logic, automata, algebra and games
Wednesday March 27, 2019, 2:15PM, 3052
Uri Zwick (Blavatnik School of Computer Science) Games on Graphs and Linear Programming Abstractions, Part 2/7: Mean Payoff games and Energy Games
https://www.irif.fr/_media/actualites/ressources/zwick_program.pdf
Logic, automata, algebra and games
Wednesday March 20, 2019, 2:15PM, 3052
Uri Zwick (Blavatnik School of Computer Science) Games on Graphs and Linear Programming Abstractions, Part 1/7: Two-player Turn-based Stochastic Games
https://www.irif.fr/_media/actualites/ressources/zwick_program.pdf
Logic, automata, algebra and games
Wednesday May 9, 2018, 2PM, 3014
Thomas Colcombet (IRIF) Superpolynomial lower bound for complementing unambiguous automata
Logic, automata, algebra and games
Wednesday March 14, 2018, 2PM, 4033
Joanna Ochremiak (Université Denis Diderot - Paris 7) Proof complexity, constraint satisfaction and graph isomorphism
Logic, automata, algebra and games
Wednesday February 14, 2018, 2PM, 4033
Joanna Ocremiak (Université Denis Diderot - Paris 7) Proof complexity, constraint satisfaction and graph isomorphism
Logic, automata, algebra and games
Thursday November 23, 2017, 10AM, 4033
Nathanaël Fijlakow (Turing Institute / CNRS) Quasi-polynomial algorithms for parity games
Logic, automata, algebra and games
Thursday June 16, 2016, 10:30AM, 4033
Florent Capelli (Liafa) Lyndon’s theorem
In this presentation, we will give a panorama of various classical preservation theorems for first-order logic. We will then present a proof of Lyndon’s theorem, and a proof that it does not hold in the finite case (this last construction is a joint work with Arnaud Durant, Amélie Gheerbrant and Cristina Sirangelo).
Logic, automata, algebra and games
Thursday February 4, 2016, 10:30AM, 4033
Christoph Haase (LSV) A Survey on Classical and Novel Results on Presburger Arithmetic
Logic, automata, algebra and games
Thursday January 21, 2016, 10:30AM, 4033
Christoph Haase (LSV) A Survey on Classical and Novel Results on Presburger Arithmetic
Logic, automata, algebra and games
Thursday January 7, 2016, 10:30AM, 4033
Sylvain Schmitz (LSV) Ideals in VAS Reachability
In this seminar, I will present the ideas behind the algorithms of Mayr, Kosaraju, and Lambert (the KLM algorithm) in the light of ideals of well-quasi-orders. The interest here is that ideals provide a semantics to the structures manipulated in the KLM algorithm, bringing some new understanding to its proof of correctness.
Joint work with Jérôme Leroux (LaBRI) presented at LICS’15; see http://arxiv.org/abs/1503.00745
Logic, automata, algebra and games
Thursday December 17, 2015, 10:30AM, 4033
Ranko Lazic (Warwick university) Rackoff’s Coverability Technique
Joint work with Sylvain Schmitz presented at RP ’15; see https://hal.inria.fr/hal-01176755/.
Logic, automata, algebra and games
Thursday December 3, 2015, 10:30AM, 2015
Sylvain Schmitz (LSV) Ideals of Well-Quasi-Orders
After defining ideals and establishing some of their properties, I will illustrate their use in a concrete setting. I will present some recent results by Czerwiński, Martens, van Rooijen, and Zeitoun (FCT’15) on the decidability of piecewise-testable separability in the light of ideals. This seminar is also a warm-up for the next seminar on reachability in vector addition systems.
Logic, automata, algebra and games
Thursday November 12, 2015, 10:30AM, 2015
Luc Segoufin (LSV) Abiteboul-Vianu theorem
The most celebrated one is Fagin’s theorem linking the complexity class NP with the expressive power of existential second-order logic.
In this lecture we will study the Abiteboul-Vianu theorem saying that the separation of PTime and PSpace can be rephrased in terms of expressive powers of partial fixpoints versus least fixpoints.
Logic, automata, algebra and games
Thursday November 5, 2015, 10:30AM, 2015
Thomas Colcombet (LIAFA) “À la Bojańcyk” proof of limitedness
In his recent LICS15 paper, Bojańczyk gave a much shorter and self-contained proof of the decidability of limitedness (and in fact also star-height). It relies on a reduction to finite games of infinite duration, and involves arguments of positionality of stragegies in quantitative games [C.&Löding08]. The topic of this talk is the presentation of this elegant proof.
The decidability of limitedness was already presented in the LAAG seminar (using the algebraic approach of stabilization monoids), but the proof here is entirely different.
Logic, automata, algebra and games
Wednesday July 1, 2015, 10AM, 4068
Stefan Göller (LSV) Decidability of DPDA equivalence, part IV
The main focus of these talks will be on the computational complexity of this problem. We will give a proof of Stirling’s result that DPDA equivalence is primitive recursive.
More precisely, we will present a recent paper by Jancar that shows that in case two DPDAs are inequivalent they can be distinguished by a word whose length is bounded by a tower of exponentials of elementary height.
As in Arnaud’s talk we will view DPDA equivalence in terms of trace equivalence of deterministic first-order grammars.
This talk aims at going hand-in-hand with Arnaud’s talk but is intended to be self-contained as well.
These talks will be completely self-contained and require no background knowledge.
Logic, automata, algebra and games
Wednesday June 17, 2015, 10:30AM, 4068
Stefan Göller (LSV) Decidability of DPDA equivalence, part III
The main focus of these talks will be on the computational complexity of this problem. We will give a proof of Stirling’s result that DPDA equivalence is primitive recursive.
More precisely, we will present a recent paper by Jancar that shows that in case two DPDAs are inequivalent they can be distinguished by a word whose length is bounded by a tower of exponentials of elementary height.
As in Arnaud’s talk we will view DPDA equivalence in terms of trace equivalence of deterministic first-order grammars.
This talk aims at going hand-in-hand with Arnaud’s talk but is intended to be self-contained as well.
These talks will be completely self-contained and require no background knowledge.
Logic, automata, algebra and games
Wednesday June 3, 2015, 10:30AM, 4068a
Arnaud Carayol (LIGM) Decidability of DPDA equivalence, part II
The aim of the talk is to present what seems to be the simplest self-contained proof of this result. We will present a proof based on the recent work of Petr Jancar which uses first-order grammars instead of deterministic pushdown automata. To keep the proof as simple as possible, we will present the proof giving two semi-decision procedures.
Logic, automata, algebra and games
Wednesday May 27, 2015, 10:30AM, 4068a
Arnaud Carayol (LIGM) Decidability of DPDA equivalence, part I
The aim of the talk is to present what seems to be the simplest self-contained proof of this result. We will present a proof based on the recent work of Petr Jancar which uses first-order grammars instead of deterministic pushdown automata. To keep the proof as simple as possible, we will present the proof giving two semi-decision procedures.
Logic, automata, algebra and games
Wednesday April 15, 2015, 10:30AM, 4067
Nathanaël Fijalkow (LIAFA) Algorithmics Properties of Probabilistic Automata, part II
The plan for this second session is:
show the decidability of two problems: the equivalence and the finiteness problem. Both proofs rely on one observation: the reals with the addition and the multiplication form a field, and some linear algebra.
Logic, automata, algebra and games
Wednesday April 1, 2015, 10:30AM, 4068
Nathanaël Fijalkow (LIAFA) The Naughty Side of Probabilistic Automata.
In this talk, I will review some of the most important undecidability results, with new simplified constructions.
Logic, automata, algebra and games
Wednesday March 11, 2015, 10:30AM, 4068
Michał Skrzypczak (LIAFA) On topology in automata theory, Part II
Logic, automata, algebra and games
Wednesday February 11, 2015, 10:30AM, 4068
Michał Skrzypczak (LIAFA) On topology in automata theory, Part I
During this talk I will introduce basic notions of topology and descriptive set theory focusing on the case of infinite words. I’ll say what is the Borel hierarchy and the Wadge order. Then I’ll show how these tools are related to automata theory. I’ll try to argue that even from purely automata theoretic point of view, it is possible to obtain new results and new proofs by referring to topological concepts.
Logic, automata, algebra and games
Wednesday January 28, 2015, 10:30AM, 4068
Gabriele Puppis (LABRI) Non-determinism vs two-way.
A classical result by Rabin and Scott shows that deterministic finite state automata are as expressive as their non-deterministic and two-way counterparts. The translation from two-way automata to one-way automata is easily seen to imply an exponential blowup in the worst case, even when one maps deterministic two-way models to non-deterministic one-way models. The converse translation, which is based on the subset construction and maps non-deterministic one-way automata to deterministic ones, also implies an exponential blowup. This latter translation, however, is not known to be optimal when one aims at removing non-determinism by possibly introducing two-wayness. In particular, the question of whether the exponential blowup is unavoidable in transforming non-determinism to two-wayness is open.
When one turns to models of transducers, some translations are not anymore possible. For example, one-way transducers (even those that exploit functional non-determinism) are easily seen to be less powerful than two-way transducers (even input-deterministic ones). A natural problem thus arises that amounts at characterizing the two-way transductions that can be implemented by one-way functional transducers. The latter problem was solved in recent paper by Filiot, Gauwin, Reynier, and Servais – however, some questions related to complexity remains open. Another interesting, but older, result by Hopcroft shows that functional non-determinism can be removed from two-way transducers, at the cost of an exponential blow-up. A similar transformation can be used to prove that two-way transducers are closed under functional composition.
Logic, automata, algebra and games
Wednesday December 17, 2014, 10:30AM, 4068
Stefan Göller (LSV) Equivalence checking of infinite state systems: A couple of lower bounds
Logic, automata, algebra and games
Wednesday December 3, 2014, 10:30AM, 4068
Thomas Colcombet (LIAFA) Stabilization monoids and cost functions
Logic, automata, algebra and games
Wednesday November 19, 2014, 10:30AM, 4068
Thomas Colcombet (LIAFA) Decidability of Boundedness and Limitedness
In this second part, we will establish the decidability of this second problem, following the ideas of Leung, Simon, and Kirsten.
Logic, automata, algebra and games
Wednesday November 5, 2014, 10:30AM, 4068
Thomas Colcombet (LIAFA) The star-height problem and its link to boundedness and limitedness
The goal of the first session is to present the famous (restricted) star-height problem, and show the first steps toward its resolution. The question is the following: given a regular language L and a non-negative integer k, can we decide whether L can bee represented as a regular expression of star-height (i.e., nesting of Kleene stars) at most k. This problem has been open for 25 years unit Hashiguchi provided a proof in a series of four paper, between 81 and 88. This proof is notoriously difficult, and the presentation here will be based on the ideas in the more modern, and much simpler, proof of Kirsten (2005).
The idea behind both these proofs is to reduce the original problem to a question of existence of bounds for a function computed by some specific forms of automata (distance automata, nested-distance desert automata, B-automata, …). This idea goes much beyond the scope of the star-height problem, and I will try to convey this idea through several examples.
Logic, automata, algebra and games
Thursday April 10, 2014, 10:30AM, 2014
David Xiao (LIAFA) Une introduction aux graphes expandeurs
Dans cet exposé nous présenterons les graphes expandeurs, leur(s) définition(s), quelques lemmes structurels fondamentaux, et quelques exemples de leur utilisation dans la dérandomisation. Nous esquisserons également la construction basée sur le produit zigzag.
Logic, automata, algebra and games
Thursday March 27, 2014, 10:30AM, 2014
Michael Vanden Boom (Oxford university) Automata characterizations of WMSO
In this talk, I will sketch the proofs showing the equivalence of WMSO and a form of automata called weak alternating automata. I will also prove Rabin’s characterization of WMSO: a language is weakly definable iff the language and its complement are recognizable by nondeterministic Büchi automata.
I will conclude by describing connections with recent work (joint with Thomas Colcombet, Denis Kuperberg, and Christof Löding) showing that given a Büchi automaton as input, it is decidable whether the language is definable in WMSO.
Logic, automata, algebra and games
Thursday March 13, 2014, 10:30AM, 2014
Olivier Serre (LIAFA) Rabin theorem
Hence, the structure of the talk will be as follows:
I will assume no specific knowledge on automata nor games for that talk.
Logic, automata, algebra and games
Saturday March 1, 2014, 10:30AM, 2014
Nathanaël Fijalkow (LIAFA) Positional determinacy part II
I will highlight the differences between the two approaches, and the applications of both techniques. In particular, I will explain why backward approaches naturally induce determinization procedures for automata over infinite words.
The talk will be self-contained, and in particular I will quickly recall all required definitions at the beginning.
Logic, automata, algebra and games
Thursday February 6, 2014, 10:30AM, 2014
Thomas Colcombet (LIAFA) Positional determinacy part I
This is in preparation to the seminars after the holidays, that will aim at presenting the results on the monadic theory of the infinite binary tree.
Logic, automata, algebra and games
Thursday December 19, 2013, 10:30AM, 4068
Sylvain Schmitz (LSV) Complexity classes beyond elementary
I plan to skim over the following topics:
The recent results will be taken from work together with S. Abriola, D. Figueira, S. Figueira, C. Haase, S. Haddad, and Ph. Schnoebelen.
Logic, automata, algebra and games
Thursday November 28, 2013, 10:30AM, 4068
Joël Ouaknine (Oxford university) Decision Problems for Linear Recurrence Sequences
This is joint work with James Worrell.
Logic, automata, algebra and games
Thursday November 7, 2013, 10:30AM, 4068
Thomas Colcombet (LIAFA) Green’s relations and automata theory
During this talk, I will present some of the key results concerning Green’s relations, emphasizing on how one can think about regular languages using them. I will also show how these can be used for deriving non-trivial automata related results (such as McNaughton’s determinization result, Schützenberger’s characterization of star-free languages, Simon’s factorization forest theorem, … though unfortunately I will not have time do to all these).
Logic, automata, algebra and games
Thursday October 17, 2013, 10:30AM, 4068
Arnaud Durand (Université Denis Diderot - Paris 7) How to count in weak formalisms?
In this talk we will evocate these different methods and present a completely elementary (and constructive) approach to reprove uniformly all these results (based on an old paper with M. More and C. Lautemann). We will also review why some of these results cannot be extended.
Logic, automata, algebra and games
Thursday June 13, 2013, 10:30AM, 4068
Łukasz Kaiser (LIAFA) Machine Learning Viewed by a Logician
Logic, automata, algebra and games
Thursday May 30, 2013, 10:30AM, 4068
Gabriele Puppis (LABRI) The Cost of Repairing Regular Specifications
The presentation is based on joint works with Michael Benedikt, Cristian Riveros, Sławek Staworko, and Pierre Bourhis.
Logic, automata, algebra and games
Thursday May 16, 2013, 10:30AM, 4068
Howard Straubing (Boston college) A New Proof of Simon’s Theorem, and Separation by Piecewise Testable Languages
Logic, automata, algebra and games
Thursday April 18, 2013, 10:30AM, 4068
Thomas Colcombet (LIAFA) Tree walking automata
In this talk, we will cover several subjects related to tree walking automata, including, the separation properties (deterministic tree walking automata are strictly weaker than non-deterministic ones [BC06], which in turn are strictly weaker than regular languages [BC08]) and closure properties (under complementation in particular [MSS06]). We will also present the models of pebble automata and relate it to first-order logic with transitive closure [EH99]. We will conclude with the separation of this logic from monadic logic over finite trees [BSSS06,BS10].
Logic, automata, algebra and games
Thursday April 4, 2013, 10:30AM, 4068
Achim Blumensath (RWTH Aachen) The Transduction Hierarchy and Definable Orderings
Logic, automata, algebra and games
Wednesday March 20, 2013, 10:30AM, 4068
Christof Löding (RWTH Aachen) Definability of uniformisation and choice in monadic second order logic
A consequence of this result is that MSO-definable relations of infinite trees cannot be uniformized in MSO (where a uniformization of a binary relation is a function that is a subset of the relation and has the same domain as the relation). One can also use the result to show that there are nondeterministic automata on infinite trees that are not equivalent to an unambiguous automaton, i.e., an automaton that has at most one accepting run for each input.
Logic, automata, algebra and games
Thursday February 21, 2013, 10:30AM, 4068
Christian Choffrut (LIAFA) Uniformization
I will not give a survey, rather talk of what I know of the topic, which is mainly binary rational relations over finite and infinite words and some connected problems.
Logic, automata, algebra and games
Thursday February 7, 2013, 10:30AM, 4068
Thomas Colcombet (LIAFA) The construction of Safra
Logic, automata, algebra and games
Thursday January 17, 2013, 10:30AM, -
Stefan Göller (LSV) Two lower bound techniques in formal verification
Second, I will recall two classical results from complexity theory (i) PSPACE is serializable meaning roughly that for determining whether a word lies in a fixed PSPACE language one only needs to check if the yield (the leaf string) of the computation tree of an NP machine lies in a fixed regular language (ii) Converting a natural number in binary to its Chinese remainder representation is in NCˆ1. I plan to use these results for proving lower bounds for reachability problems and model checking problems for one-counter automata and timed automata, respectively.
Logic, automata, algebra and games
Thursday December 20, 2012, 10:30AM, -
Sam Van Gool (LIAFA) A topological proof of Gödel’s completeness theorem for first-order logic
Logic, automata, algebra and games
Thursday December 13, 2012, 10:30AM, -
Colin Riba (ENS Lyon) A Model Theoretic Proof of Completeness of an Axiomatization of Monadic Second-Order Logic on Infinite Words
Logic, automata, algebra and games
Thursday June 14, 2012, 10:30AM, -
Frédéric Magniez (LIAFA) An Introduction to Communication Complexity
Logic, automata, algebra and games
Thursday May 31, 2012, 10:30AM, -
Thomas Colcombet (LIAFA) The collapse of monadic second order logic over countable linear orderings
Logic, automata, algebra and games
Thursday May 10, 2012, 10:30AM, -
Thomas Colcombet (LIAFA) The monadic theory of orderings
Logic, automata, algebra and games
Thursday May 3, 2012, 10:30AM, -
Michel De Rougemont (LIAFA) Games for Monadic Σ11 (EMSO) and probabilistic methods
Logic, automata, algebra and games
Thursday April 12, 2012, 10:30AM, -
Olivier Carton (LIAFA) Kamp's theorem
Logic, automata, algebra and games
Monday March 26, 2012, 10:30AM, submarine
Achim Blumensath (LIAFA) Stability theory