September 30 Alessandro Facchini Max=Muller, up to Wadge equivalence Recently, Mikolaj Bojanczyk introduced a class of max-regular languages, an extension of regular languages of infinite words preserving many of its usual properties. This new class can be seen as a different way of generalizing the notion of regularity from finite to infinite words. This paper compares regular and max-regular languages in terms of topological complexity. It is proved that up to Wadge equivalence the classes coincide. Moreover, when restricted to $\mathbf{\Delta}^0_2$-languages, the classes contain virtually the same languages. On the other hand, separating examples of arbitrary complexity exceeding $\mathbf{\Delta}^0_2$ are constructed. June 17 Dariusz Dereniowski On some searching problems and related graph parameters During this talk we focus on some graph searching problems. There exist several interesting connections between graph searching and graph parameters. As an example one can mention the correspondence between the minimum number of searchers required to clear a graph and pathwidth or treewidth. We are interested in some new and less examined properties. In particular, we consider, for a search strategy, the maximum vertex occupation time, i.e. the maximum number of steps a vertex is occupied (guarded) by a searcher. The corresponding graph parameter is called treespan and is closely related to the concept of elimination trees. As a second problem example we investigate a connection between the graph ranking problem (a model of graph coloring) and the maximum number of queries necessary to find an element in tree-like partial orders and partial orders with maximum element. May 27 Marcin Bilkowski Unambiguous tree languages I will talk about the class of unambiguous regular languages of trees. For every language in this class there exists an automaton that accepts this language and admits at most one successful run for every tree. I will show that not all regular languages on trees are unambiguous. I will also show a few classes of languages that are ambiguous. May 13, 20 Szymon Toruńczyk Deciding emptiness of min-automata I will present an algorithm which verifies emptiness of min-automata. This problem is equivalent to the problem of limitedness of Distance Automata and the finite section problem for the semiring of matrices over the (+,min) semiring, both of which were considered by Hashiguchi, Leung and Simon. I will present a proof of correctness based on a proof by Kirsten (which, in turn, originates from Leung). I will also show that the problem is PSpace-complete. May 6 Mikołaj Bojańczyk An automaton for XPath (joint work with Slawomir Lasota) I will talk about an automaton model for Xpath. The new model can capture many boolean queries of XPath (in particular, all queries of FOXPath). Consequently, emptiness is undecidable. Nevertheless, the automaton seems interesting for the following reasons. a) Model checking (query evaluation) is decidable, and automata methods could be used to derive efficient algorithms for XPath using this model. b) By restricting the class of models to some class X (such as bounded tree-width), emptiness for XPath becomes decidable again. To understand which classes X are a good idea, it helps to work with automata instead of formulas. c) Some nice techniques are used to show how XPath can be captured by the automaton. April 29 Paweł Parys XPath evaluation in linear time We consider a fragment of XPath where attribute values can be tested for equality (FOXPath). We show that for any fixed unary query in this fragment, the set of nodes that satisfy the query can be calculated in time linear in the document size and polynomial in the query size. When we allow arbitrary regular expressions in path expressions, the complexity in the query size is exponential. April 22 Dexter Kozen (Cornell) On the Coalgebraic Theory of Kleene Algebra with Tests We develop a coalgebraic theory of Kleene algebra with tests (KAT) along the lines of Rutten (1998) for Kleene algebra and Chen and Pucella (2003) for a limited version of KAT, resolving two open problems of Chen and Pucella. Our treatment includes a simple definition of the Brzozowski derivative for KAT expressions and an automata-theoretic interpretation involving automata on guarded strings. We also give a complexity analysis, showing that an efficient implementation of coinductive equivalence proofs in this setting is essentially equivalent to standard automata-theoretic constructions. It follows that coinductive equivalence proofs can be generated automatically in PSPACE. This matches the bound of Worthington (2008) for the automatic generation of equational proofs in KAT. April 1 Wojciech Czerwiński (joint work with Sławomir Lasota) Partially Commutative Context Free Processes (cont.) March 25 Paweł Parys (joint work with Igor Walukiewicz) Weak Alternating Timed Automata Alternating timed automata on infinite words are considered. The main result is the characterization of acceptance conditions for which the emptiness problem for the automata is decidable. This result implies new decidability results for fragments of timed temporal logics. It is also shown that, unlike for some logics, the characterisation remains the same even if no punctual constrains are allowed. March 18 Wojciech Czerwiński (joint work with Sławomir Lasota) Partially Commutative Context Free Processes I will talk about some new class of processes (transition systems) which could be useful for investigating properties of the Process Algebra (PA), a well known class of transition systems. In particular I will show language differences between PA and PCCFP and shortly describe a new algorithm for testing bisimulation in PCCFP. March 11 Mikołaj Bojańczyk (joint work with Tomasz Idziaszek and Wojciech Czerwiński) Forest algebra for infinite forests I will talk about an extension of forest algebra for ω-forests. We show how the standard algebraic notions (free object, syntactic algebra, morphisms, etc) extend to the infinite case. To prove its usefulness, I will use the framework to get an effective characterization of the ω-forest languages that are definable in the temporal logic that uses the operator EF (exists finally). March 4 Szymon Toruńczyk (joint work with Mikołaj Bojańczyk) Min-regular languages A new class of languages of infinite words is introduced, called the min-regular languages, extending the class of omega-regular languages. Min-regular languages are somehow dual to max-regular languages introduced before. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter automaton), and in terms of logic (weak monadic second-order logic with a bounding quantifier). February 25 Paweł Parys Lower bound for computing fixed points We consider the following problem: There is given a monotone K-argument function f defined on N-bit sequences {0,1}^N. There is also given the following simpliest possible mu-calculus expression: mi(x1).ni(x2).mi(x3).ni(x4)...mi(xK).f(x1,...,xK). The function is given as a black-box: we can only query it for given arguments. The question is how many queries are necessary to calculate the value of the expression? The goal would be to show an exponential (in N and K) lower bound. I will show that for K=2 almost N^2 queries are needed. February 18 Łukasz Kaiser (Aachen) Basic Analysis of Structure Rewriting Systems A single state of an analyzed system has, in practice, often a complex structure in itself, while in theory it is usually simple in some sense, e.g. it can be a tree. We show how the interpretation of structures of bounded clique-width in the binary tree allows to apply tree automata to the analysis of a basic kind of systems where states are arbitrary relational structures. A few new questions emerge for more general systems, and we discuss them as well. January 21 Henryk Michalewski Complete pairs of coanalytic sets January 6 Mikołaj Bojańczyk A geometrical approach to star height I will talk about an algorithm deciding limitedness of distance desert automata (which is the hard part in deciding star height). The algorithm itself is quite simple, and the correctness argument involves concepts such as compact metric space and convergent sequence. December 10, 17 Tomasz Idziaszek EF logic I will talk about a simple temporal logic EF over finite words, infinite words and finite trees. I will show that a language is definable by an EF formula if and only if its syntactic algebra satisfies certain equations. Eventually I will present some examples which exhibit the difficulty of EF over infinite trees. December 3 Leszek Kołodziejczyk Parity games in weak arithmetic theories Parity games in weak arithmetic theories I will present A. Beckmann and F. Moller's paper "On the complexity of parity games". The main result of the paper is that positional determinacy of parity games can be proved in a weak subtheory of Peano Arithmetic called S^2_2. The provability of determinacy in a still weaker theory, S^1_2, would mean that the problem of deciding which player wins from a given position in a parity game is in P. The current result implies that the problem of finding a winning strategy is in the class PLS (polynomial local search). November 26 Mikołaj Bojańczyk The star-height problem November 5 Tomasz Jurdziński (Wrocław) Leftist grammars Leftist grammars were introduced as a tool to show decidability of the accessibility problem in certain general protection systems. In the presentation, I will concentrate on complexity of the membership problem for these grammars and their restricted variants. October 22, 29 Mikołaj Bojańczyk Max-regular languages (cont.) October 17, room 4010 Thomas Wilke (Kiel) Contract Signing Protocols: A Playground for Temporal (and other Modal) Logics in Information Security October 8 Mikołaj Bojańczyk Max-regular languages A new class of languages of infinite words is introduced, called the max-regular languages, extending the class of omega-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter automaton), and in terms of logic (weak monadic second-order logic with a bounding quantifier). Effective translations between the logic and automata are given. October 1 How to do cryptography on non-trusted machines? Stefan Dziembowski (Rome)

Most of the real-life attacks on cryptographic devices do not break their mathematical foundations, but exploit vulnerabilities of their implementations. This concerns both the cryptographic software executed on PCs (that can be attacked by viruses), and the implementations on hardware (that can be subject to the side-channel attacks). Traditionally fixing this problem was left to the practitioners, since it was a common belief that theory cannot be of any help here. However, new exciting results in cryptography suggest that this view was too pessimistic: there exist methods to design cryptographic protocols in such a way that they are secure even if the hardware on which they are executed cannot be fully trusted.

We will give a brief overview of some of those methods, concentrating on the theory of the bounded-retrieval model (see e.g. [1,2])

[1] S. Dziembowski and K. Pietrzak. Intrusion-Resilient Secret Sharing, FOCS 2007.

[1] S. Dziembowski and K. Pietrzak. Leakage-Resilient Cryptography in the Standard Model, accepted to FOCS 2008.

June 20On Borel Inseparability of Game Tree LanguagesSzczepan Hummel June 4 Thomas Colcombet's deterministic version of Simon's decomposition theorem Aymeric Vincent

In this presentation, we will introduce Simon's decomposition theorem and give an outline of the proof given by Thomas Colcombet. We will then concentrate on a weaker version of the theorem which has the advantage of being "deterministic" in the sense that the decomposition of any prefix of a word does not depend on its suffix.

The work of Thomas was published in 2007 at FCT and ICALP, but we follow his research report containing the proofs "On Factorization Forests", also from 2007.

 May 28 New Directions in Preference Research Jan Chomicki (Buffalo)

I will survey several recently proposed applications and extensions of a logical approach to preference specification and querying. In that approach, preferences are defined as binary relations that are finitely representable using first-order formulas. Preference querying is done using the winnow operator that picks the "best" tuples in a given relation.

First, I will discuss the operation of discarding preferences: preference contraction. Minimality and preservation of strict partial orders (SPOs) seem to be crucial in this context. I will show how to construct minimal SPO-preserving contractions, both for finite and finitely-representable preference relations.

Second, I will describe a logical framework for set preferences. Candidate sets are represented using profiles consisting of scalar features. This reduces set preferences to tuple preferences over set profiles. I will also discuss a heuristic algorithm for the computation of the ``best'' sets.

This is joint work with my Ph.D. students: Denis Mindolin and Xi Zhang.

 May 7 Eliminating randomness from infinite games Eryk Kopczyński Consider infinite games played on a graph by two antagonistic players Eve and Adam. Each position in the game graph belongs to one of two players, who decides which move he or she takes; the winner is decided based on the infinite play. This model can be extended in several ways: introducing "random" positions where the next move is chosen randomly; letting the game result to be any value in a bounded subset of reals instead of win or loss; or positions where the two players simultaneously choose their next action, and the move chosen depends on these two actions. I will show how these extensions reduce to the basic model. As a side result we get that the Axiom of Determinacy implies that all sets are Lebesgue measurable. The talk is partly based on works of D. A. Martin. April 30 What is a regular language of data words? Mikołaj Bojańczyk It is impossible to define an automaton model for data words that would simultaneously satisfy several reasonable requirements, such as closure under boolean operations, decidable emptiness, etc. I will present some attempts that have appeared to this day, and compare their relative shortcomings. April 16, 23 XPath evaluation in linear time Paweł Parys We consider a fragment of XPath where attribute values can only be tested for equality (FOXPath). We show that for any fixed unary query in this fragment, the set of nodes that satisfy the query can be calculated in time linear in the document size. April 2 The Insecurity Problem: Tackling Unbounded Data Sybille Froeschle (Oldenburg)

In this talk we focus on tackling the insecurity problem of security protocols in the presence of an unbounded number of data such as nonces or session keys. First, we pinpoint four open problems in this category. The first two problems concern protocols with natural restrictions that any `realistic' protocol should satisfy while the second two concern protocols with disequality constraints. For protocols with disequality constraints we will prove: (1) Insecurity is decidable in NEXPTIME when bounding the size of messages and not requiring data to be \emph{freshly} generated. (2) Insecurity is NEXPTIME-complete when bounding the size of messages and the number of freshly generated data used in honest sessions. This shows that unbounded data can be tackled in settings which do not trivially reduce to the case of bounded data.

March 28 The nondeterministic Mostowski hierarchy and distance-parity automata Christof Loeding (Aachen)

The number of priorities that nondeterministic Mostowski or parity automata on infinite trees can use in their acceptance condition induces a hierarchy of regular tree languages. This talk is about the problem of deciding for a given regular language of infinite trees on which level of the hierarchy it is. I will present a reduction of this problem to the uniform universality problem for distance-parity automata. The latter model is an extension of nested distance desert automata introduced by D. Kirsten in the proof of decidability of the star-height problem for languages of finite words. Distance-parity automata do not simply accept or reject trees but assign to each tree a cost (a natural number or infinity). The uniform universality problem is the question whether the cost function computed by a given distance-parity automaton is bounded by some natural number. It is still open in the general case whether this problem is decidable, but we already know how to solve it for a subclass of distance-parity automata.

 March 19 Property testing regular languages Szymon Toruńczyk

Property testing is concerned with the following type of problems: Let L be a property of a class of objects. A property tester for L is an algorithm, which, given an input object w, uses a small number of (possibly random) queries about w to determine with high probability whether w has the property L or whether it is far from having it.

I will present a result of Alon et al. stating that membership of a word w in a given regular language L is testable with a constant (dependent on L but not on w) number of queries to w.

I will also discuss a result of Magniez and Rougemont on testability of membership in regular languages of trees.

 March 5, 12 Lossy Machines Sławomir Lasota

FIFO- and counter-automata are Turing complete models. I will present a weakening of these models, allowing for spontaneous and non-controllable loss of messages from FIFO (or, respectively, decrements of counters). I will discuss how much this weakening decreases complexity of verification problems, like reachability, termination, equivalence and model-checking.

 February 27 Weak index versus Borel rank Filip Murlak

I will talk about weak recognizability of deterministic languages of infinite trees. I will prove that for deterministic languages the Borel hierarchy and the weak index hierarchy coincide. Furthermore, I will propose a procedure computing for a deterministic automaton an equivalent minimal index weak automaton with a quadratic number of states.

 January 16, 23 Mec 5 and AltaRica Aymeric Vincent

In this presentation, we will present the Mec 5 verification tool and its environment. In particular, we will talk about the AltaRica formalism which has been developed in Bordeaux for more than ten years. We will then focus on two aspects of Mec 5:

- its technical basis, mainly BDDs. We will try to show what we learned from our experimentations with BDDs in the last years

- its very powerful logic which allows to express for example bisimilarity between two models, and we will show here how to use this logic to compute the winning strategies in parity games.

 January 9 The polynomial and linear time hierachies in a weak theory of arithmeticLeszek KolodziejczykI will show that a very weak theory of arithmetic associated with the complexity class AC^0 does not prove that the polynomial time hierarchy is equal to the linear time hierarchy. The proof uses Ajtai's old bounds on how well polysize bounded depth circuits can compute parity. 28 November, 5 December Automatic groups, continuedAndrzej Nagorko 21 November Games with priorities Wieslaw Zielonka 14 November Automatic groupsAndrzej NagorkoI'll talk about automatic groups, which incorporate finite state automata into geometric group theory in a prolific way. The class of automatic groups was introduced by Cannon and Thurston in the eighties. 7 NovemberAutomata and logics for data valuesMikolaj BojanczykAn XML document is commonly modeled as a tree, with nodes labeled by a finite alphabet. Properties of such documents can be expressed using finite tree automata, which are well understood and admit efficient algorithms. However, the finite alphabet representation does not capture some aspects of a document, such as references or keys. It is not clear how to add these features, while still retaining the benefits of finite automata. I will talk about recent work in this direction. 24 OctoberSimulation between gamesWojciech Czerwinski I will show some results of my investigations on bisimulation with a weakened winning condition for Spoiler. I will present a polynomial algorithm deciding this (modified) bisimulation between Buchi games. I will also talk about positionality, and other types of bisimulation. 17 October Lindstrom theorems for fragments of first-order logicBalder ten Cate (joint work with J. van Benthem and J. Vaananen) Lindstrom theorems characterize logics in terms of model-theoretic conditions such as Compactness and the Loewenheim-Skolem property. Most existing Lindstrom theorems concern extensions of first-order logic. On the other hand, many logics relevant to computer science are fragments or extensions of fragments of first-order logic, e.g., k-variable logics and various modal logics. Finding Lindstrom theorems for these languages can be challenging, as most known techniques rely on coding arguments that seem to require the full expressive power of first-order logic.
In this paper, we provide Lindstrom characterizations for a number of fragments of first-order logic. These include the k-variable fragments for k > 2, Tarski's relation algebra, graded modal logic, and the binary guarded fragment. We use two different proof techniques. One is a modification of the original Lindstrom proof. The other involves the modal concepts of bisimulation, tree unraveling, and finite depth. Our results also imply semantic preservation theorems. Characterizing the 2-variable fragment or the full guarded fragment remain open problems. 10 October Algorithms for Solving Simple Stochastic GamesHugo Gimbert (joint work with F. Horn) A Simple Stochastic Game is played by two players called Min and Max, moving turn by turn a pebble along edges of a graph. Player Max wants the pebble to reach a special vertexc called the target vertex. On some special vertices called random vertices, the next vertex is chosen randomly according to some fixed transition probabilities.
Solving a simple stochastic game consists in computing the maximal probability with which player Max can enforce the pebble to reach the target vertex.
In this talk, we will present several known algorithms for solving such games, as well as a new algorithm specially designed for games with few random vertices. 30 May Generalization of Binary Search: Searching in Trees and Forest-Like Partial OrdersPaweł Parys (joint work with Krzysztof Onak) We extend the binary search technique to searching in trees. We consider two models of queries: questions about vertices and questions about edges. We present a general approach to this sort of problem, and apply it to both cases, achieving algorithms constructing optimal decision trees. In the edge query model the problem is identical to the problem of searching in a special class of tree-like posets stated by Ben-Asher, Farchi and Newman [1]. Our upper bound on computation time, O(n^3), improves the previous best known O(n^4 log n). In the vertex query model we show how to compute an optimal strategy much faster, in O(n) steps. We also present an almost optimal approximation algorithm for another class of tree-like (and forest-like) partial orders. 23 May Probalistically Checkable Proofs and approximation hardness (continued)Anna Niewiarowska 16 May Conjunctive grammarsArtur Jeż I discuss the notion of conjunctive grammars, introduced by A. Okhotin in 2001. In short they can be described as extension of context-free grammars with additional operation of intersection within the body of any production. This natural extension still leads to inheriting many nice properties from context-free grammars, in particular easy parsing algorithm. On the other hand it allows us to define more languages.
I will also talk about my small contribution solving the problem of expressing power of unary conjunctive grammars, that is over unary alphabet. It is easy to show, that the context-free grammars can only define regular languages over unary alphabet. I will show that this is not true in case of conjunctive grammars and also show some consequences for decision problems of unary conjunctive grammars. 9 May Probalistically Checkable Proofs and approximation hardnessAnna Niewiarowska The PCP theorem states that for each NP language there is a verifier that checks membership proofs probabilistically, using only logaritmic number of random bits and reading constant number of proof bits. I will show that many approximation hardness results are consequences of that theorem. I will also show the idea of the proof of the PCP theorem. 25 April Forest expressionsMikołaj Bojańczyk I will talk about a type of regular expression for unranked trees. The main focus is on connections with logic: the expressions correspond to chain logic, the star-free expressions correspond to first-order logic, and finally, a concatenation hierarchy is shown to correspond to the quantifier alternation hierarchy. 18 April Undecidability methods for the word problem in finite semigroupsKonrad Zdanowski 3 April Two remarks on the role of ranks in parity gamesDamian Niwiński These observations are of very different nature, but they can be read as evidences for the lower bound, and the upper bound, respectively. At first we show that the number of ranks gives rise to a strict hierarchy of the parity-game tree languages, in the sense of Wadge reducibility. Next, we observe that the algorithm for solving parity game need not always depend exponentially on the number of ranks. 28 MarchLuc Segoufin (Paris) A view of a database is a query which is precomputed. When a new query comes in it is natural to wonder whether it can be answered with what is already computed. In other work we ask whether the views carry enough information for answering the query. We will see that this question is intimately connected with implicit versus explicit definability. If our databases where infinite, Beth's theorem would be of great help. But we work in the finite and this is where the story gets interesting... 21 MarchTemporal Logics and Model Checking for Fairly Correct SystemsFilip Murlak I will present recent results on model checking for fairly correct systems (D. Varacca, H. Voelzer, LICS'06). A fair variant of a specfication is obtained by replacing "for all paths" by "for a large set of paths". For regular linear-time specifications, probabilistic and topological largness coincide. Hence, by results on probabilistic model checking, fair variants of LTL, omega-regular, and CTL* specifications are not harder to check than the originals. For CTL, the linear model checking algorithm can be adapted to the fair variant. 14 March On Systems of Equations Satisfied in All Commutative Finite SemigroupsPawel Parys I show the algorithmic procedure for solving the problem: check if a system of equations has a solution in every commutative finite semigroup. 28 February A paradox for CTL Mikołaj Bojańczyk The property "every path belongs to (ab)*a(ab)*" can be expressed in CTL; but necessarily using existential modalities. This shows that ACTL;does not capture the common fragment of CTL and LTL. 17 January Tomasz Kazana I will show that the following problem is decidable: "For a given regular language L, decide if every word has a cycle in L?". Recall that a word u is a cycle of a word w if w=(u^n)v, for some n >= 1, and some prefix v of u.
The result is a particular case for an open problem in programming language theory. 10 JanuaryIntroducing equations in free semigroupRobert Dąbrowski Let be given a free monoid with a set of generators E whose cardinality is at least 2. We shall call elements of E 'letters' and elements of E* 'words'. Let also be given a set of 'unknowns'; disjoint with letters. A 'word expression' is defined recursively to be either a letter, an unknown or a nonempty finite sequence of word expressions. A 'word equation' is then of the form L=R where L, R are word expressions. A 'solution' to a word equation is any mapping from the unknowns into (possible empty) words which makes L and R identical words.
The fundamental problem for equations in free monoids ('word equations') is to decide if a solution exists. The problem apparently had its source with Markov and remained open for a considerable period. The more general problem is finding a convenient description of all solutions.
I will first present some fundamental constructions and results that allow to investigate word equations. Then I will summarize current results in respect to deciding solvability and finding solutions. I will focus on the cases with a fixed number of variables. Examples will follow. 3 JanuaryMaria FraczakDefining rational functions by deterministic pushdown transducers Rational functions are partial functions from words to words. They are implemented by finite state automata extended to produce output; only some of them can be realized by deterministic pushdown transducers (deterministic pushdown automata producing output). I will present several classes of rational functions that can be realized by deterministic pushdown transducers of various kinds. 20 DecemberBisimulation equivalence and commutative context-free grammars Sławomir LasotaThe topic will be the class of processes (transition systems) generated from the commutative context-free grammars. I will present a method enabling to prove decidability (and to compute the complexity) of different variants of bisimulation equivalence for the abovementioned class. 6 December Thomas Schwentick 29 NovemberTwo-way temporal logic over unranked treesMikołaj BojańczykI will talk about languages of unranked trees that can be defined in a temporal logic with two operators: exists some ancestor, and exists some descendant. The point is to have an algorithm, which decides if a given regular tree language can be expressed by a formula of this logic. 23 November12:15, room 5870 Subexponential algorithms for solving parity gamesMarcin Jurdziński Solving parity games is polynomial time equivalent to the modal mu-calculus model checking problem and its exact computational complexity is an intriguing open problem: it is known to be in UP (unambiguous NP) and co-UP, but no polynomial time algorithm is known. This talk surveys a few recent algorithmic ideas which yield improved running time bounds for the problem. One is obtained by a reduction of parity games to the problem of finding the unique sink in a "unique sink orientation" of a hypercube and it yields a subexponential randomized algorithm. The other is a modification of a classical recursive algorithm for solving parity games that originates from the work of McNaughton and Zielonka and it yields a subexponential deterministic algorithm. 15 NovemberWeak automata and Wadge hierarchyFilip Murlak I will show a new lower bound for the height of the Wadge hierarchy of weak tree languages, i. e., the languages of infinite trees recognizable with weak automata. To this end I will prove that the family of weak tree languages is closed by three natural set-theoretic operations that can be used to climb up the hierarchy starting from the simplest sets. 25 October, 8 NovemberPanic automata Jacek Jurewicz Panic automata are an extension of second-order pushdown automata (that operate on a second-order pushdown store, ie. a stack of stacks) by the destructive "panic" operation introduced by P. Urzyczyn in order to fully relate second-order automata to second-order grammars.
I will show how a panic automaton (and a non-panic second-order automaton in particular) can be efficiently simulated by a multitape Turing machine, with the preservation of determinism, in spite of a possible quadratic growth of the store. In this case, efficiency means that the length of a run of the machine is proportional to the length of a run of the automaton, which need not be proportional to the size of the input. The result is achieved by introducing an encoding of the pushdown store by a string. Interestingly, while the proof holds for ordinary second-order automata, the encoding relies on additional information stored in the stack, invented exclusively for the "panic" operation. 11, 18 October Half-positionally determined winning conditionsEryk KopczynskiBasic definitions: games, half-positional determinacy. - Half-positional winning conditions and omega-regular languages. How to check whether the given omega-regular winning condition is finitely half-positional? - Positional/suspendable conditions (PS). Definitions and examples. Half-positional determinacy of a countable union on PS conditions, and of the winning conditions in the class XPS (extended positional/suspendable conditions). 4 October Toward Regular Data LanguagesHenrik Bjorklund (Dortmund) 7 JuneThe computational dichotomy of true-concurrencySibylle Froeschle In concurrency theory there is a divide between the interleaving approach, in which concurrency is reduced to nondeterministic sequentialization, and the truly-concurrent approach, which represents concurrency in a more faithful way. In this talk I will give an inroduction to true-concurrency, and survey results and open problems in the area. In particular I will address the computational dichotomy of true-concurrency: for finite-state systems truly-concurrent paradigms are typically computationally harder than their interleaving counterparts while for restricted finite-state as well as infinite- state classes this effect is often reversed. 31 MayWord problemsPiotr Hoffman The talk will be an introduction to the world of word problems, in particular word problems for varieties of semigroups. Attention will be paid especially to commutative semigroups (reversible Petri nets). I intend to prove Redei's Theorem on finitely generated commutative semigroups and, if time allows, the decidability of the (uniform) word problem for commutative semigroups and the undecidability of the uniform word problem for finite semigroups. 24 May Impossibility Proofs for Distributed ComputingMichał Strojnowski Many problems have no solution in distributed computing. One of the best known examples is Byzantine Generals Problem, for which it is shown that if at least one third of the generals are malicious, there is no way to achieve mutual consensus among the rest. There are many more such examples, especially where randomization and asynchronization is considered. Techniques used to show impossibility are sometimes very interesting, and may be applied in areas different from distributed computing.
This presentation will be based on a classical paper of Nancy Lynch, in which she managed to collect over a hundred of such proofs. Some of them are in fact lower bounds, that show some problems unsolvable with limited resources. Of course only a few particularly interesting proofs will be presented. 10 May On language and bisimulation equivalence of context-free processesSlawomir Lasota (joint work with Wojciech Rytter) In contrast to language equivalence, being undecidable for (normed) context-free grammars, the bisimulation equivalence is decidable; and it is even polynomial for normed grammars.The fastest known algorithm for checking bisimulation equivalence worked in $O(n^{13})$ time. We give an alternative algorithm working in $O(n^8 \polylog\ n)$ and $O(n^2\;v)$ time, where $v$ is the maximum norm of a process. Thus we make a step towards a low complexity algorithmic solution of the bisimulation equivalence problem. As a side effect we improve the best known upper bound for testing equivalence of simple context-free grammars from $O(n^7 \polylog\ n)$ to $O(n^6 \polylog\ n)$. 26 AprilTableaux for Regular Grammar Logics of Agents Using Automaton-Modal FormulaeLinh Anh Nguyen (joint work with Rajeev Gore) A grammar logic is a multimodal logic extending Kn with inclusion axioms of the form
[t1]...[th]j (r) [s1]...[sk]j
where t1, ..., th, s1, ..., sk are modal indices. Such an axiom can be seen as the grammar rule
t1...th (r) s1...sk
where the corresponding side stands for the empty word if k = 0 or h = 0. Thus the inclusion axioms of a grammar logic L capture a grammar G(L). This grammar is context-free if its rules are of the form
t (r) s1...sk
and is regular if it is context-free and for every modal index t there exists a finite automaton At that recognises the words derivable from t using G(L). A regular grammar logic L is a grammar logic whose inclusion axioms correspond to grammar rules that collectively capture a regular grammar G(L).
We present sound and complete tableau calculi for the class of regular grammar logics and a class eRG of extended regular grammar logics which contains useful epistemic logics for reasoning about beliefs of agents. Our tableau rules use a special feature called automaton-modal formulae which are similar to formulae of automaton propositional dynamic logic. Our calculi are cut-free and have the analytic superformula property so they give decision procedures. We show that the known EXPTIME upper bound for regular grammar logics can be obtained using our tableau calculus. We also prove that the general satisfiability problem of eRG logics is EXPTIME-complete. http://www.mimuw.edu.pl/%7enguyen/gn05jar.pdf" 29 March, 5, 12 AprilReachability in vector-addition systems Mikolaj Bojanczyk An (n-dimensional) vector addition system is a finite set V of n-dimensional integer vectors. The reachability problem is as follows: given V and two n-dimensional vectors of *naturals * v and w, determine if one can produce a sequence v=v(1),v(2),..,v(k)=w of vectors of naturals, such that each difference v(i+1) - v(i) -- which need not be a vector of naturals -- belongs to the set V. I will try to describe Kosaraju's algorithm, which solves this problem. 22 MarchWord problems in sums of monoids Piotr Hoffman In the talk I will investigate the decidability of word problems for amalgams (sums) of monoids. Word problems for amalgams of monoids are equivalent to sums of congruence relations on words. They are also equivalent to unions of equational theories over signatures in which only unary function symbols appear.
In particular I will show:
- decidability for cases in which the intersection monoid is a group or group with zero,
- undecidability for a case in which the intersection is a 3-elementn right-zero monoid,
- undecidability for an amalgam of finite monoids.
If time allows, I will also describe my work with Mikolaj Bojanczyk on
amalgams of commutative monoids. 15 MarchPositional Stochastic StrategiesHugo Gimbert We present ongoing work on positionality of full-information, two-player, zero-sum stochastic games with finitely many states. 3 MarchAttention! Friday 14:15, 5820Logic with two variables and equivalence relations Emanuel Kieronski (Wroclaw, joint work with Martin Otto) We study first-order logic with two variables FO2 and establish a small substructure property. Similar to the small model property for FO2 we obtain an exponential size bound on embedded substructures, relative to a fixed surrounding structure that may be infinite. We apply this technique to analyse the satisfiability problem for FO2 under constraints that require several binary relations to be interpreted as equivalence relations. With a single equivalence relation, FO2 has the finite model property and is complete for non-deterministic exponential time, just as for plain FO2. With two equivalence relations, FO2 does not have the finite model property, but is shown to be decidable via a construction of regular models that admit finite descriptions even though they may necessarily be infinite. For three or more equivalence relations, FO2 is undecidable. 22 FebruaryData wordsMikolaj Bojanczyk (Joint work with C. David, A. Muscholl, L. Segoufin and T. Schwentick. ) A data word is a word that is annotated with data values. Every position in a data word has the usual label from a finite alphabet, but it also has a label from an infinite set. Access to the second coordinate - called the data value - is restricted.
We present a decidable automaton model for data words. Interestingly enough, this model reaches far beyond regular languages: emptiness for our automata is equivalent to reachability in Petri nets. We also present a decidable logic for reasoning about data words, this is a type of two-variable first-order logic. 18, 25 JanuaryGames for the Wadge Hierarchy of Deterministic Tree LanguagesFilip Murlak In the case of infinite words, the hierarchy of regular languages defined by continuous reductions is well understood since Wagner's 1977 paper. In particular, there exists a procedure calculating the exact level of a given language in the Wadge hierarchy. We will consider an analogous problem for tree languages. In the case of languages of infinite words, there exists a continuous reduction from L to M, iff Duplicator has a winning strategy in the Wadge game G(L,M). For recognizable languages, an equivalent criterion is the existance of a finite-state transducer reducing L to M. The last property is no more true for trees. However, we manage to adapt the Wadge games to the case of deterministically recognizable tree languages in such a way that the crucial property is maintained. We reinterpret this game entirely in terms of automata recognisnig the languages and using this tool we provide an effective description of the Wadge hierarchy of deterministic tree languages. 14 December, 11 January Half-positionally determined winning conditions in infinite gamesEryk Kopczynski We consider half-positionally determined winning conditions in infinite games played on a graph by two antagonistic players Eve and Adam. We call a winning condition W _positionally determined_ if, for every infinite game (G,W) using this winning condition, one of the players has a positional (i.e. memoryless) winning strategy. We call a winning condition _half-positionally determined_ if we only require Eve's strategy to be positional, but Adam's strategy can be arbitrary.
We will show some general properties of such winning conditions. While some properties of positionally determined conditions can be easily generalized to the case of half-positional determinacy, some cannot. We will also show some classes of half-positionally determined winning conditions; these classes are independent (none of them is included in another) and include:
* Concave winning conditions, which, among others, include (generalized) parity conditions and Rabin conditions. Concavity is sufficient for half-positional determinacy only in case of games on finite arenas;
* Geometric conditions, associated with convex subsets of [0,1]^n;
* Monotonic winning conditions, given by a deterministic finite automaton with a monotonic transition function. 7 December Infnite games on finite graphsThomas Colcombet (Rennes) We consider games played on an arena (a graph) by two antagonistic players. In such a game, each player, when there is its turn, chooses an edge to follow, originating in the current position. The next position is the destination of this edge. After an infinite number of turns, an infinite path has been chosen, and the winner of the game is decided by checking the conformance of this infinite path to a criterion fixed in advance: the winning condition.
Sometimes, the winner of the game can win by playing according to a positional strategy, i.e. a strategy where the next move is decided solely depending on the current position in the game, (and not on the history of the current play). Some winning conditions are known to ensure the existence of a positional strategy for the winner (e.g. parity conditions or mean-payoff conditions over finite arenas). Such situations have important algorithmic impact and deep implications in automata theory.
In this talk, we present the basic concepts of this theory of games and aim toward a complete characterization of winning conditions entailing positional strategies for the winner over _finite_ arenas (though we are not able to give a complete answer to this question).
This is joint work with Damian Niwinski. 30 NovemberOne-clock timed automataSlawomir Lasota For timed automata with two clocks emptyness in decidable but universality and containment are not. We will show that all these problems are decidable for alternating timed automata, but with only one clock. The non-primitive-recursive complexity will be shown. On infinite words, universality (and containment) will be shown undecidable for one-clock Buechi automata. We will also discuss relationships with timed temporal logics, possible extensions of our results and open problems. 23 NovemberComplexity of bisimulation equivalenceSlawomir Lasota An overview of known results and open problems in checking bisimulation equivalence on infinite graphs. In particular, graphs generated by context-free grammars and pushdown automata will be considered. Relationship to language equivalence will be pointed out, in particular for deterministic pushdown automata and for so called simple grammars. 18 November Attention! Friday 14:15, room 3230DAG-width and Parity Games Stephan Kreutzer Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Tree-width is characterised by a game known as the cops-and-robber game where a number of cops chase a robber on the graph. We consider the natural adaptation of this game to directed graphs and show that monotone strategies in the game yield a measure with an associated notion of graph decomposition that can be seen to describe how close a directed graph is to a directed acyclic graph (DAG). This promises to be useful in developing algorithms on directed graphs. In particular, we show that the problem of determining the winner of a parity game is solvable in polynomial time on graphs of bounded DAG-width. We also consider the relationship between DAG-width and other measures of such as entanglement and directed tree-width. One consequence we obtain is that certain NP-complete problems such as Hamiltonicity and disjoint paths are polynomial-time computable on graphs of bounded DAG-width. 2 NovemberPositional Payoff Games Hugo Gimbert (joint work with Wieslaw Zielonka) I will present some results about the existence of positional optimal strategies in two-players antagonistic games and of positional Nash equilibria in multiplayer games. 19, 26 OctoberModel checking of panic automataDamian Niwinski (joint work with T. Knapik, P. Urzyczyn, and I. Walukiewicz) Panic automata, invented by Pawel Urzyczyn, extend the concept of 2nd order pushdown automata (with stacks of stacks), by a destructive move called panic. They are in a sense equivalent to 2nd order tree grammars. We show the decidability, in fact, 2-EXPTIME-completeness, of the Mu-calculus model-checking problem for the configuration graphs of such automata. This implies decidability of the monadic second-order theories of hyperalgebraic trees, the result independently obtained by Aehlig, de Miranda and Ong. 5, 12 OctoberUnranked Tree AlgebraMikolaj Bojanczyk (joint with Igor Walukiewicz) I will present an algebra for recognizing languages of unranked, finite trees. This algebra is a special case of a transformation semigroup. The talk will focus on analyzing algebras that correspond to languages defined in logic (for instance, first-order logic)