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22
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
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 23 (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
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 23 (0 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.
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 18 (8 self)
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We consider an extension of modal logic with an operator for constructing...
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 13 (0 self)
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The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper
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 12 (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.
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 10 (1 self)
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We survey evaluation games for firstorder logic and least fixed point logics, and discuss their algorithmic complexity.
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 10 (4 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.
Notes on the Propositional µcalculus: Completeness and Related Results
, 1995
"... Contents 1 Introduction 1 1.1 Synopsis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 Preliminaries 3 2.1 Syntax and semantics of the calculus : : : : : : : : : : : : : : : 3 2.2 Restrictions and extensions of the syntax : : : : : : : : : : : : : 4 2.3 Binding definitions : : ..."
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Cited by 5 (0 self)
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Contents 1 Introduction 1 1.1 Synopsis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 Preliminaries 3 2.1 Syntax and semantics of the calculus : : : : : : : : : : : : : : : 3 2.2 Restrictions and extensions of the syntax : : : : : : : : : : : : : 4 2.3 Binding definitions : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.4 Automata on infinite objects : : : : : : : : : : : : : : : : : : : : 7 3 Tableaux, markings and "operational semantics" 10 3.1 Formulas as automata : : : : : : : : : : : : : : : : : : : : : : : : 10 3.2 Formalisation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 4 Applications of operational semantics 21 4.1 Small model theorem, decidability, syntactic characterisations : : 21 4.2 Tableau equivalence : : : : : : : :