The theory of ends, pushdown automata, and second-order logic

Muller, David E.; Schupp, Paul E.

doi:10.1016/0304-3975(85)90087-8

Cited by 277 publications

(204 citation statements)

References 3 publications

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“…The decidability of the model-checking problem for pushdown processes and the propositional µ-calculus follows from [18]. This decidability result as well as extensions of it (for example [7]) deal with monadic second order logic and reduce the problem to the decidability of S2S, hence give nonelementary algorithms.…”

Section: Introductionmentioning

confidence: 88%

Pushdown processes: Games and model checking

Walukiewicz

1996

Lecture Notes in Computer Science

108

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A pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton. A winning condition in such a game is defined in terms of states appearing infinitely often in the play. It is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a pushdown automaton. An EXPTIME procedure for finding a winner in a pushdown game is presented. The procedure is then used to solve the model-checking problem for the pushdown processes and the propositional µ-calculus. The problem is shown to be DEXPTIME-complete.

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Section: Introductionmentioning

confidence: 88%

Pushdown processes: Games and model checking

Walukiewicz

1996

Lecture Notes in Computer Science

108

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“…In this way, one obtains, e.g., the classes of automatic [Hod83,KN95,BG00] and tree-automatic [DT90,BG00] structures, for which the FOtheory is decidable, and the classes of pushdown-graphs [MS85] and prefix recognizable graphs [Cau96] with decidable MSO-theory. …”

Section: Introductionmentioning

confidence: 99%

Transforming structures by set interpretations

Colcombet¹,

Löding²

2007

Logical Methods in Computer Science

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Abstract. We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable first-order theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and tree-automatic structures.

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“…Similar suggestions to extend the expressiveness of CTL ¡ are studied in the literature. This includes both the extensions of the path formulas of CTL ¡ with © -regular word automata [VW84,CGK92], and the extension of the state formulas with © -regular tree automata [MS85]. As in the linear framework, one can strengthen these extensions by using more powerful automata, in particular two-way and alternating ones.…”

Section: Discussionmentioning

confidence: 99%

Extended Temporal Logic Revisited

Kupferman

Piterman

Vardi

2001

Lecture Notes in Computer Science

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Abstract.A key issue in the design of a model-checking tool is the choice of the formal language with which properties are specified. It is now recognized that a good language should extend linear temporal logic with the ability to specify all -regular properties. Also, designers, who are familiar with finite-state machines, prefer extensions based on automata than these based on fixed points or propositional quantification. Early extensions of linear temporal logic with automata use nondeterministic Büchi automata. Their drawback has been inability to refer to the past and the asymmetrical structure of nondeterministic automata. In this work we study an extension of linear temporal logic, called ETL © , that uses two-way alternating automata as temporal connectives. Two-way automata can traverse the input word back and forth and they are exponentially more succinct than one-way automata. Alternating automata combine existential and universal branching and they are exponentially more succinct than nondeterministic automata. The rich structure of two-way alternating automata makes ETL © a very powerful and convenient logic. We show that ETL © formulas can be translated to nondeterministic Büchi automata with an exponential blow up. It follows that the satisfiability and model-checking problems for ETL © are PSPACEcomplete, as are the ones for LTL and its earlier extensions with automata. So, in spite of the succinctness of two-way and alternating automata, the advantages of ETL © are obtained without a major increase in space complexity. The recent acceptance of alternating automata by the industry and the development of symbolic procedures for handling them make us optimistic about the practicality of ETL © .

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The theory of ends, pushdown automata, and second-order logic

Cited by 277 publications

References 3 publications

Pushdown processes: Games and model checking

Pushdown processes: Games and model checking

Transforming structures by set interpretations

Extended Temporal Logic Revisited

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