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.
|Title of host publication
|Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings
|Ed Brinksma, Kim Guldstrand Larsen
|Number of pages
|Published - 2002
|14th International Conference on Computer Aided Verification, CAV 2002 - Copenhagen, Denmark
Duration: 27 Jul 2002 → 31 Jul 2002
|Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
|14th International Conference on Computer Aided Verification, CAV 2002
|27/07/02 → 31/07/02
Bibliographical notePublisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.