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32
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
Completeness of Kozen's Axiomatisation of the Propositional µCalculus
 Inform. and Comput
, 1995
"... Propositional calculus is an extension of the propositional modal logic with the least fixpoint operator. In the paper introducing the logic Kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the modal system K. It is shown that this ..."
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Cited by 33 (1 self)
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Propositional calculus is an extension of the propositional modal logic with the least fixpoint operator. In the paper introducing the logic Kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the modal system K. It is shown that this axiomatisation is complete.
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
Inflationary Fixed Points in Modal Logic
, 2002
"... We consider an extension of modal logic with an operator for constructing... ..."
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Cited by 26 (9 self)
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We consider an extension of modal logic with an operator for constructing...
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.
A Complete Deductive System for the µCalculus
, 1995
"... The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper ..."
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Cited by 14 (0 self)
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The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper
Model Checking Games
, 2002
"... We survey evaluation games for firstorder logic and least fixed point logics, and discuss their algorithmic complexity. ..."
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Cited by 12 (1 self)
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We survey evaluation games for firstorder logic and least fixed point logics, and discuss their algorithmic complexity.
Continuous separation of game languages
, 2006
"... We show that a family of tree languages W(';^), previously used by J. Brado/eld, and by the o/rst author to show the strictness of the Mostowski index hierarchy of alternating tree automata, forms a hierarchy w.r.t. the Wadge reducibility. That is, W(';^) ^W W('0;^0) if and only if ..."
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Cited by 9 (1 self)
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We show that a family of tree languages W(';^), previously used by J. Brado/eld, and by the o/rst author to show the strictness of the Mostowski index hierarchy of alternating tree automata, forms a hierarchy w.r.t. the Wadge reducibility. That is, W(';^) ^W W('0;^0) if and only if the index ('0; ^0) is above ('; ^). This is one of the few separation results known so far, concerning the topological complexity of nondeterministically recognizable tree languages, and one of the few results about finitestate recognizable nonBorel sets of trees. The interest of the result is reinforced by the fact that a related family M(';^), witnessing the strictness of the index hierarchy of nondeterministic automata, does not have a similar property.
Decidable Properties of Tree Languages
, 2004
"... The first part of the thesis concerns problems related to the question: “when can a regular tree language be defined in firstorder logic? ” Characterizations in terms of automata of firstorder logic and the related chain logic are presented. A decidable property of tree automata called confusion i ..."
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Cited by 9 (6 self)
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The first part of the thesis concerns problems related to the question: “when can a regular tree language be defined in firstorder logic? ” Characterizations in terms of automata of firstorder logic and the related chain logic are presented. A decidable property of tree automata called confusion is introduced; it is conjectured that a regular tree language can be defined in chain logic if and only if its minimal automaton does not contain confusion. Furthermore, polynomial time algorithms are presented that decide if a given regular tree language can be defined in any one of the temporal branching logics TL[EX], TL[EF] and TL[EX, EF]. In the second part of the thesis, an extension MSOL+B of monadic secondorder logic over infinite trees is considered, where a new quantifier B is added. Using this quantifier, one can express properties such as: “there exist bigger and bigger sets satisfying... ” An automatatheoretic investigation of the quantifier is conducted, yielding decidable satisfiability for two fragments of MSOL+B. These results are then applied to a decision problem stemming from the µcalculus.