TY - GEN

T1 - An automata-theoretic approach to infinite-state systems

AU - Kupferman, Orna

AU - Piterman, Nir

AU - Vardi, Moshe Y.

PY - 2010

Y1 - 2010

N2 - In this paper we develop an automata-theoretic framework for reasoning about infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that a system satisfies a temporal property can then be done by an alternating two-way tree automaton that navigates through the tree. We show how this framework can be used to solve the model-checking problem for μ-calculus and LTL specifications with respect to pushdown and prefix-recognizable systems. In order to handle model checking of linear-time specifications, we introduce and study path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. As has been the case with finite-state systems, the automata-theoretic framework is quite versatile. We demonstrate it by solving the realizability and synthesis problems for μ-calculus specifications with respect to prefix-recognizable environments, and extending our framework to handle systems with regular labeling regular fairness constraints and μ-calculus with backward modalities.

AB - In this paper we develop an automata-theoretic framework for reasoning about infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that a system satisfies a temporal property can then be done by an alternating two-way tree automaton that navigates through the tree. We show how this framework can be used to solve the model-checking problem for μ-calculus and LTL specifications with respect to pushdown and prefix-recognizable systems. In order to handle model checking of linear-time specifications, we introduce and study path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. As has been the case with finite-state systems, the automata-theoretic framework is quite versatile. We demonstrate it by solving the realizability and synthesis problems for μ-calculus specifications with respect to prefix-recognizable environments, and extending our framework to handle systems with regular labeling regular fairness constraints and μ-calculus with backward modalities.

UR - http://www.scopus.com/inward/record.url?scp=77955020949&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-13754-9_11

DO - 10.1007/978-3-642-13754-9_11

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AN - SCOPUS:77955020949

SN - 3642137539

SN - 9783642137532

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 202

EP - 259

BT - Time for Verification - Essays in Memory of Amir Pnueli

A2 - Manna, Zohar

A2 - Peled, Doron A.

ER -