Model Checking Linear Properties of Prefix-Recognizable Systems

  • Authors:

  • Orna Kupferman;Nir Piterman;Moshe Y. Vardi

  • Affiliations:

  • -;-;-

  • Venue:
  • CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
  • Year:
  • 2002

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Abstract

We develop an automata-theoretic framework for reasoning about linear properties of 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 the system satisfies a temporal property can then be done by an alternating two-way automaton that navigates through the tree. We introduce 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. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems.We demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and we prove a matching lower bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.