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17
Quantitative Stochastic Parity Games
"... We study perfectinformation stochastic parity games. These are twoplayer nonterminating games which are played on a graph with turnbased probabilistic transitions. A play results in an infinite path and the conflicting goals of the two players are!regular path properties, formalized as parity w ..."
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Cited by 51 (22 self)
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We study perfectinformation stochastic parity games. These are twoplayer nonterminating games which are played on a graph with turnbased probabilistic transitions. A play results in an infinite path and the conflicting goals of the two players are!regular path properties, formalized as parity winning conditions. The qualitative solution of such a game amounts to computing the set of vertices from which a player has a strategy to win with probability 1 (or with positive probability). The quantitative solution amounts to computing the value of the game in every vertex, i.e., the highest probability with which a player can guarantee satisfaction of his own objective in a play that starts from the vertex. For the important special case of oneplayer stochastic parity games (parity Markov decision processes) we give polynomialtime algorithms both for the qualitative and the quantitative solution. The running time of the qualitative solution is O(d \Delta m 3=2) for graphs with m edges and d priorities. The quantitative solution is based on a linearprogramming formulation.
Coalgebraic automata theory: Basic results
 Logical Methods in Computer Science
"... Vol. 4 (4:10) 2008, pp. 1–43 www.lmcsonline.org ..."
Perfectinformation Stochastic Parity Games
, 2004
"... We show that in perfectinformation stochastic parity games with a finite state space both players have optimal pure positional strategies. Contrary to the recent proofs of this fact by K. Chatterejee, M. Jurdziński, T.A. Henzinger [2] and A.K. McIver, C.C. Morgan [14] the proof given in this paper ..."
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Cited by 11 (0 self)
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We show that in perfectinformation stochastic parity games with a finite state space both players have optimal pure positional strategies. Contrary to the recent proofs of this fact by K. Chatterejee, M. Jurdziński, T.A. Henzinger [2] and A.K. McIver, C.C. Morgan [14] the proof given in this paper proceeds by a straightforward induction on the number of outgoing transitions available to one of the players and is selfcontained.
Completions of µalgebras
 In Proceedings of the Twentieth Annual IEEE Symposium on Logic in Computer Science (LICS 2005
, 2005
"... A µalgebra is a model of a first order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms (f, µx.f) where µx.f is axiomatized as the least prefixed point of f, whose axioms are equations or equational implications. Standard µalgebras are complete meaning ..."
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Cited by 8 (2 self)
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A µalgebra is a model of a first order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms (f, µx.f) where µx.f is axiomatized as the least prefixed point of f, whose axioms are equations or equational implications. Standard µalgebras are complete meaning that their lattice reduct is a complete lattice. We prove that any non trivial quasivariety of µalgebras contains a µalgebra that has no embedding into a complete µalgebra. We focus then on modal µalgebras, i.e. algebraic models of the propositional modal µcalculus. We prove that free modal µalgebras satisfy a condition – reminiscent of Whitman’s condition for free lattices – which allows us to prove that (i) modal operators are adjoints on free modal µalgebras, (ii) least prefixed points of Σ1operations satisfy the constructive relation µx.f = W n≥0 f n (⊥). These properties imply the following statement: the MacNeilleDedekind completion of a free modal µalgebra is a complete modal µalgebra and moreover the canonical embedding preserves all the operations in the class Comp(Σ1, Π1) of the fixed point alternation hierarchy.
On computing fixpoints in wellstructured regular model checking, with applications to lossy channel systems
 In Proc. LPAR’2006
, 2006
"... Abstract. We prove a general finite convergence theorem for “upwardguarded” fixpoint expressions over a wellquasiordered set. This has immediate applications in regular model checking of wellstructured systems, where a main issue is the eventual convergence of fixpoint computations. In particula ..."
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Cited by 5 (0 self)
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Abstract. We prove a general finite convergence theorem for “upwardguarded” fixpoint expressions over a wellquasiordered set. This has immediate applications in regular model checking of wellstructured systems, where a main issue is the eventual convergence of fixpoint computations. In particular, we are able to directly obtain several new decidability results on lossy channel systems. 1
Undirected graphs of entanglement 2
, 2007
"... Abstract. Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at ..."
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Cited by 4 (2 self)
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Abstract. Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at most k. As this measure is defined by means of games, game theoretic ideas naturally lead to design polynomial algorithms that, for fixed k, decide the problem. Known characterizations of directed graphs of entanglement at most 1 lead, for k = 1, to design even faster algorithms. In this paper we give two distinct characterizations of undirected graphs of entanglement at most 2. With these characterizations at hand, we present a linear time algorithm to decide whether an undirected graph has this property. 1
A Parametric Analysis of the StateExplosion Problem in Model Checking ⋆
"... In model checking, the stateexplosion problem occurs when one checks a nonflat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of modelchecking problems for nonflat systems under the lig ..."
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Cited by 3 (0 self)
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In model checking, the stateexplosion problem occurs when one checks a nonflat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of modelchecking problems for nonflat systems under the light of parameterized complexity, taking the number of synchronized components as a parameter. We provide precise complexity measures (in the parameterized sense) for most of the problems we investigate, and evidence that the results are robust. 1
Completeness for Flat Modal Fixpoint Logics (Extended Abstract)
"... Abstract. Given a set Γ of modal formulas of the form γ(x, p), where x occurs positively in γ, the language L♯(Γ) is obtained by adding to the language of polymodal logic K connectives ♯γ, γ ∈ Γ. Each term ♯γ is meant to be interpreted as the parametrized least fixed point of the functional interpre ..."
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Cited by 2 (2 self)
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Abstract. Given a set Γ of modal formulas of the form γ(x, p), where x occurs positively in γ, the language L♯(Γ) is obtained by adding to the language of polymodal logic K connectives ♯γ, γ ∈ Γ. Each term ♯γ is meant to be interpreted as the parametrized least fixed point of the functional interpretation of the term γ(x). Given such a Γ, we construct an axiom system K♯(Γ) which is sound and complete w.r.t. the concrete interpretation of the language L♯(Γ) on Kripke frames. If Γ is finite, then K♯(Γ) is a finite set of axioms and inference rules.
Partially commutative inverse monoids
 PROCEEDINGS OF THE 31TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 2006), BRATISLAVE (SLOVAKIA), NUMBER 4162 IN LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... Free partially commutative inverse monoids are investigated. Analogously to free partially commutative monoids (trace monoids), free partially commutative inverse monoid are the quotients of free inverse monoids modulo a partially defined commutation relation on the generators. An O(n log(n)) algo ..."
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Cited by 2 (2 self)
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Free partially commutative inverse monoids are investigated. Analogously to free partially commutative monoids (trace monoids), free partially commutative inverse monoid are the quotients of free inverse monoids modulo a partially defined commutation relation on the generators. An O(n log(n)) algorithm on a RAM for the word problem is presented, and NPcompleteness of the generalized word problem and the membership problem for rational sets is shown. Moreover, free partially commutative inverse monoids modulo a finite idempotent presentation are studied. For these monoids, the word problem is decidable if and only if the complement of the commutation relation is transitive.
An invitation to play
"... Parity games and their subclasses and variants pop up in various contexts: µcalculus, tree automata, program verification [3, 1, 8]. Such games provide only binary information indicating the winning player. However, in classical games theory [12] the emphasis is rather on how much we win or lose. ..."
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Cited by 2 (1 self)
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Parity games and their subclasses and variants pop up in various contexts: µcalculus, tree automata, program verification [3, 1, 8]. Such games provide only binary information indicating the winning player. However, in classical games theory [12] the emphasis is rather on how much we win or lose. Can we incorporate the information about the profits and losses into parity games?