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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
Automated Temporal Reasoning about Reactive Systems
, 1996
"... . There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective a ..."
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Cited by 41 (2 self)
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. There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective and reliable means of specifying and ensuring correct behavior of such systems. This paper discusses known complexity and expressiveness results for a number of such logics in common use and describes key technical tools for obtaining essentially optimal mechanical reasoning algorithms. However, the emphasis is on underlying intuitions and broad themes rather than technical intricacies. 1 Introduction There is a growing need for reliable methods of designing correct reactive systems. These systems are characterized by ongoing, typically nonterminating and highly nondeterministic behavior. Examples include operating systems, network protocols, and air traffic control systems. There is w...
A Kleene Theorem and Model Checking Algorithms for Existentially Bounded Communicating Automata
 INFORMATION AND COMPUTATION 204:920–956
, 2006
"... The behavior of a network of communicating automata is called existentially bounded if communication events can be scheduled in such a way that the number of messages in transit is always bounded by a value that depends only on the machine, not the run itself. We show a Kleene theorem for existentia ..."
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Cited by 26 (7 self)
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The behavior of a network of communicating automata is called existentially bounded if communication events can be scheduled in such a way that the number of messages in transit is always bounded by a value that depends only on the machine, not the run itself. We show a Kleene theorem for existentially bounded communicating automata, namely the equivalence between communicating automata, globallycooperative compositional message sequence graphs, and monadic second order logic. Our characterization extends results for universally bounded models, where for each and every possible scheduling of communication events, the number of messages in transit is uniformly bounded [15, 17]. As a consequence, we give solutions in the spirit of [22] for various model checking problems on networks of communicating automata that satisfy our optimistic restriction.
Logical Aspects of CayleyGraphs: The Group Case
 TO APPEAR IN ANNALS OF PURE AND APPLIED LOGIC
"... We prove that a finitely generated group is contextfree whenever its Cayleygraph has a decidable monadic secondorder theory. Hence, by the seminal work of Muller and Schupp, our result gives a logical characterization of contextfree groups and also proves a conjecture of Schupp. To derive this re ..."
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Cited by 12 (3 self)
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We prove that a finitely generated group is contextfree whenever its Cayleygraph has a decidable monadic secondorder theory. Hence, by the seminal work of Muller and Schupp, our result gives a logical characterization of contextfree groups and also proves a conjecture of Schupp. To derive this result, we investigate general graphs and show that a graph of bounded degree with a high degree of symmetry is contextfree whenever its monadic secondorder theory is decidable. Further, it is shown that the word problem of a finitely generated group is decidable if and only if the firstorder theory of its Cayleygraph is decidable.
Automatic structures of bounded degree revisited
, 2008
"... The firstorder theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary firstorder theories. We prove that the firstorder theory of a string automatic structure of bounded degree is decidable in doubly exponential s ..."
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Cited by 6 (4 self)
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The firstorder theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary firstorder theories. We prove that the firstorder theory of a string automatic structure of bounded degree is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). This result is shown to be optimal since we also present a string automatic structure of bounded degree whose firstorder theory is hard for 2EXPSPACE. We prove similar results also for tree automatic structures. These findings close the gaps left open in [24] by improving both, the lower and the upper bounds.
Automata and Logic
, 2002
"... Contents 1 Introduction 2 2 Finite words 4 2.1 Firstorder and monadic secondorder logics . . . . . . . . . . 4 2.2 Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Infinite words 10 3.1 Closure properties of #automata . . . . . . . . . . . . . . . . 14 4 Infinite trees 21 4 ..."
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Cited by 2 (0 self)
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Contents 1 Introduction 2 2 Finite words 4 2.1 Firstorder and monadic secondorder logics . . . . . . . . . . 4 2.2 Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Infinite words 10 3.1 Closure properties of #automata . . . . . . . . . . . . . . . . 14 4 Infinite trees 21 4.1 Closure properties of tree automata . . . . . . . . . . . . . . . 23 4.2 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5 The calculus and alternating automata 28 5.1 Syntax and semantics of the calculus . . . . . . . . . . . . . 28 5.2 Alternating automata . . . . . . . . . . . . . . . . . . . . . . . 30 5.3 From the calculus to alternating automata . . . . . . . . . . 32 LaBRI, Domaine Universitaire, btiment A30, 351, cours de la Libration, 33405 Talence Cedex, FRANCE. email:igw@labri.fr; www: http://www.labri.fr/#igw These are notes for EFF Summer School, July 2001, with minor modifications. 5.4 From alternating automata to the calculus . . . . . . . .
The Boundary between Decidable and Undecidable Fragments of the Fluent Calculus
, 2000
"... We consider entailment problems in the fluent calculus as they arise in reasoning about actions. Taking into account various fragments of the fluent calculus we formally show decidability results, establish their complexity, and prove undecidability results. Thus we draw a boundary between decidable ..."
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We consider entailment problems in the fluent calculus as they arise in reasoning about actions. Taking into account various fragments of the fluent calculus we formally show decidability results, establish their complexity, and prove undecidability results. Thus we draw a boundary between decidable and undecidable fragments of the fluent calculus.
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"... e = f, where e and f are both idempotents in the free inverse monoid generated by \Gamma. Itis shown that for every fixed monoid of this form the word problem can be solved in polynomial time which solves an open problem of Margolis and Meakin. For the uniform word problem, where thepresentation is ..."
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e = f, where e and f are both idempotents in the free inverse monoid generated by \Gamma. Itis shown that for every fixed monoid of this form the word problem can be solved in polynomial time which solves an open problem of Margolis and Meakin. For the uniform word problem, where thepresentation is part of the input, EXPTIMEcompleteness is shown. For the Cayleygraphs of these monoids, it is shown that the firstorder theory with regular path predicates is decidable. Regular pathpredicates allow to state that there is a path from a node