An automata-theoretic approach to infinite-state systems

  • Authors:

  • Orna Kupferman;Nir Piterman;Moshe Y. Vardi

  • Affiliations:

  • Hebrew University, School of Engineering and Computer Science, Jerusalem, Israel;Imperial College London, Department of Computing, London, UK;Rice University, Department of Computer Science, Houston, TX

  • Venue:
  • Time for verification
  • Year:
  • 2010

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Abstract

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.