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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 186 (7 self)
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Games given by transition graphs of pushdown processes are considered. It is shown that
LOGICS FOR UNRANKED TREES: AN OVERVIEW
 CONSIDERED FOR PUBLICATION IN LOGICAL METHODS IN COMPUTER SCIENCE
, 2006
"... Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to ..."
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Cited by 40 (7 self)
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Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their modelchecking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees.
Complete axiomatization and decidability of alternatingtime temporal logic
 Theor. Comput. Sci
"... Alternatingtime Temporal Logic (ATL), introduced by Alur, Henzinger and Kupferman, is a logical formalism for the specification and verification of open systems involving multiple autonomous players (agents, components). In particular, this logic allows for the explicit expression of coalition abi ..."
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Cited by 38 (5 self)
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Alternatingtime Temporal Logic (ATL), introduced by Alur, Henzinger and Kupferman, is a logical formalism for the specification and verification of open systems involving multiple autonomous players (agents, components). In particular, this logic allows for the explicit expression of coalition abilities in such systems, modelled as infinite transition games between the coalition and its complement. Formally, ATL is a nonnormal multimodal extension of CTL (regarded as a oneplayer fragment of ATL) with temporal operators indexed by coalitions of players, and thus expressing selective quantification over those paths which can be effected as outcomes of infinite transition games between the coalition and its complement. We present a sound and complete axiomatization of the logic ATL, based on Pauly’s axiomatization of his Coalition Logic, augmented with axioms and rules for fixed point formulae characterizing the temporal operators. The completeness proof is by construction of a bounded branching tree model for eachATLconsistent formula. These models can be folded into finite models, thus rendering the finite model property for ATL. We also describe an automatabased decision procedure for ATL by translating the satisfiability problem to the nonemptiness problem for alternating automata on infinite trees. When considering formulae over a fixed finite set of players the decidability problem is shown to be EXPTIMEcomplete.
Finite Model Theory and Descriptive Complexity
, 2002
"... This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the ..."
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Cited by 27 (7 self)
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This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the
Complete sequent calculi for induction and infinite descent
 Proceedings of LICS22
, 2007
"... This paper compares two different styles of reasoning with inductively defined predicates, each style being encapsulated by a corresponding sequent calculus proof system. The first system supports traditional proof by induction, with induction rules formulated as sequent rules for introducing induct ..."
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Cited by 25 (8 self)
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This paper compares two different styles of reasoning with inductively defined predicates, each style being encapsulated by a corresponding sequent calculus proof system. The first system supports traditional proof by induction, with induction rules formulated as sequent rules for introducing inductively defined predicates on the left of sequents. We show this system to be cutfree complete with respect to a natural class of Henkin models; the eliminability of cut follows as a corollary. The second system uses infinite (nonwellfounded) proofs to represent arguments by infinite descent. In this system, the left rules for inductively defined predicates are simple casesplit rules, and an infinitary, global condition on proof trees is required to ensure soundness. We show this system to be cutfree complete with respect to standard models, and again infer the eliminability of cut. The second infinitary system is unsuitable for formal reasoning. However, it has a natural restriction to proofs given by regular trees, i.e. to those proofs representable by finite graphs. This restricted “cyclic ” system subsumes the first system for proof by induction. We conjecture that the two systems are in fact equivalent, i.e., that proof by induction is equivalent to regular proof by infinite descent.
Representations of stream processors using nested fixed points
 Logical Methods in Computer Science
"... Abstract. We define representations of continuous functions on infinite streams of discrete values, both in the case of discretevalued functions, and in the case of streamvalued functions. We define also an operation on the representations of two continuous functions between streams that yields a ..."
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Cited by 24 (2 self)
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Abstract. We define representations of continuous functions on infinite streams of discrete values, both in the case of discretevalued functions, and in the case of streamvalued functions. We define also an operation on the representations of two continuous functions between streams that yields a representation of their composite. In the case of discretevalued functions, the representatives are wellfounded (finitepath) trees of a certain kind. The underlying idea can be traced back to Brouwer’s justification of barinduction, or to Kreisel and Troelstra’s elimination of choicesequences. In the case of streamvalued functions, the representatives are nonwellfounded trees pieced together in a coinductive fashion from wellfounded trees. The definition requires an alternating fixpoint construction of some ubiquity.
A Gap Property of Deterministic Tree Languages
"... We show that a tree language recognized by a deterministic parity automaton is either hard for the coBüchi level and therefore cannot be recognized by a weak alternating automaton, or is on a very low level in the hierarchy of weak alternating automata. We also give a new simple proof of the strict ..."
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Cited by 22 (4 self)
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We show that a tree language recognized by a deterministic parity automaton is either hard for the coBüchi level and therefore cannot be recognized by a weak alternating automaton, or is on a very low level in the hierarchy of weak alternating automata. We also give a new simple proof of the strictness of the hierarchy of weak alternating automata.
The variable hierarchy of the µcalculus is strict
 STACS 2005, PROCEEDINGS OF THE 22ND SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE. VOLUME 3404 OF LNCS., SPRINGERVERLAG
, 2005
"... Most of the logics commonly used in verification, such as LTL, CTL, CTL∗, and PDL can be embedded into the twovariable fragment of the µcalculus. It is also known that properties occurring at arbitrarily high levels of the alternation hierarchy can be formalised using only two variables. This rais ..."
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Cited by 18 (4 self)
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Most of the logics commonly used in verification, such as LTL, CTL, CTL∗, and PDL can be embedded into the twovariable fragment of the µcalculus. It is also known that properties occurring at arbitrarily high levels of the alternation hierarchy can be formalised using only two variables. This raises the question whether the number of fixedpoint variables in µformulae can be bounded in general. We answer this question negatively, and prove that the variablehierarchy of the µcalculus is semantically strict. For any k, we provide examples of formulae with k variables that are not equivalent to any formula with fewer variables. In particular, this implies that Parikh’s Game Logic is less expressive than the µcalculus, thus resolving an open issue raised by Parikh in 1983.