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Pushdown Processes: Games and Model Checking
, 1996
"... Games given by transition graphs of pushdown processes are considered. It is shown that ..."
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Cited by 136 (4 self)
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Games given by transition graphs of pushdown processes are considered. It is shown that
Guarded Fixed Point Logic
, 1999
"... Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andr eka, van Benthem and N emeti. Guarded fixed point logics can also be viewed as the natural common extensions of the modal µcalculus an ..."
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Cited by 58 (4 self)
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Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andr eka, van Benthem and N emeti. Guarded fixed point logics can also be viewed as the natural common extensions of the modal µcalculus and the guarded fragments. We prove that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time. For guarded fixed point sentences of bounded width, the most important case for applications, the satisfiability problem is EXPTIMEcomplete.
How Much Memory is Needed to Win Infinite Games?
, 1997
"... We consider a class of infinite twoplayer games on finitely coloured graphs. Our main question is: given a winning condition, what is the inherent blowup (additional memory) of the size of the I/O automata realizing winning strategies in games with this condition. This problem is relevant to synth ..."
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Cited by 43 (1 self)
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We consider a class of infinite twoplayer games on finitely coloured graphs. Our main question is: given a winning condition, what is the inherent blowup (additional memory) of the size of the I/O automata realizing winning strategies in games with this condition. This problem is relevant to synthesis of reactive programs and to the theory of automata on infinite objects. We provide matching upper and lower bounds for the size of memory needed by winning strategies in games with a fixed winning condition. We also show that in the general case the LAR (latest appearance record) data structure of Gurevich and Harrington is optimal. Then we propose a more succinct way of representing winning strategies by means of parallel compositions of transition systems. We study the question: which classes of winning conditions admit only polynomialsize blowup of strategies in this representation. 1 Introduction We consider games played on (not necessarily finite) graphs coloured with a finite nu...
Monadic SecondOrder Logic, Graph Coverings and Unfoldings of Transition Systems
"... We prove that every monadic secondorder property of the unfolding of a transition system is a monadic secondorder property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for ..."
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Cited by 27 (6 self)
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We prove that every monadic secondorder property of the unfolding of a transition system is a monadic secondorder property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for one of them but not for the other.
Monadic Second Order Logic on TreeLike Structures
, 1996
"... An operation M* which constructs from a given structure M a treelike structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such treelike structures is defined. It is shown that automata of this kind characterise expressive power of ..."
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Cited by 19 (6 self)
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An operation M* which constructs from a given structure M a treelike structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such treelike structures is defined. It is shown that automata of this kind characterise expressive power of monadic second order logic (MSOL) over treelike structures. Using this characterisation it is proved that MSOL theory of treelike structures is effectively reducible to that of the original structures. As another application of the characterisation it is shown that MSOL on trees of arbitrary degree is equivalent to first order logic extended with unary least fixpoint operator.
Automata and fixed point logics: a coalgebraic perspective
 Electronic Notes in Theoretical Computer Science
, 2004
"... This paper generalizes existing connections between automata and logic to a coalgebraic level. Let F: Set → Set be a standard functor that preserves weak pullbacks. We introduce various notions of Fautomata, devices that operate on pointed Fcoalgebras. The criterion under which such an automaton a ..."
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Cited by 15 (7 self)
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This paper generalizes existing connections between automata and logic to a coalgebraic level. Let F: Set → Set be a standard functor that preserves weak pullbacks. We introduce various notions of Fautomata, devices that operate on pointed Fcoalgebras. The criterion under which such an automaton accepts or rejects a pointed coalgebra is formulated in terms of an infinite twoplayer graph game. We also introduce a language of coalgebraic fixed point logic for Fcoalgebras, and we provide a game semantics for this language. Finally we show that any formula p of the language can be transformed into an Fautomaton Ap which is equivalent to p in the sense that Ap accepts precisely those pointed Fcoalgebras in which p holds.
Games where you can play optimally without any memory
 In CONCUR 2005, LNCS
, 2005
"... Abstract. Reactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently how ..."
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Cited by 13 (4 self)
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Abstract. Reactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently however also games with other types of payments, like discounted or meanpayoff [5,6], previously used only in economic context, entered into the area of system modelling and verification. The most outstanding property of parity, meanpayoff and discounted games is the existence of optimal positional (memoryless) strategies for both players. This observation raises two questions: (1) can we characterise the family of payoff mappings for which there always exist optimal positional strategies for both players and (2) are there other payoff mappings with practical or theoretical interest and admitting optimal positional strategies. This paper provides a complete answer to the first question by presenting a simple necessary and sufficient condition on payoff mapping guaranteeing the existence of optimal positional strategies. As a corollary to this result we show the following remarkable property of payoff mappings: if both players have optimal positional strategies when playing solitary oneplayer games then also they have optimal positional strategies for twoplayer games.
Coalgebraic automata theory: Basic results
 Logical Methods in Computer Science
"... Vol. 4 (4:10) 2008, pp. 1–43 www.lmcsonline.org ..."
When can you play positionally
 In Mathematical Foundations of Computer Science 2004, volume 3153 of LNCS
, 2004
"... Abstract. We consider infinite antagonistic games over finite graphs. We present conditions that, whenever satisfied by the payoff mapping, assure for both players positional (memoryless) optimal strategies. To verify the robustness of our conditions we show that all popular payoff mappings, such as ..."
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Cited by 8 (4 self)
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Abstract. We consider infinite antagonistic games over finite graphs. We present conditions that, whenever satisfied by the payoff mapping, assure for both players positional (memoryless) optimal strategies. To verify the robustness of our conditions we show that all popular payoff mappings, such as mean payoff, discounted, parity as well as several other payoffs satisfy them. 1