An automata-theoretic approach to infinite-state systems

Orna Kupferman*, Nir Piterman, Moshe Y. Vardi

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

18 Scopus citations

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.

Original languageAmerican English
Title of host publicationTime for Verification - Essays in Memory of Amir Pnueli
EditorsZohar Manna, Doron A. Peled
Pages202-259
Number of pages58
DOIs
StatePublished - 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6200 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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