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 the system satisfies a temporal property can then be done by an alternating two-way tree automaton that navigates through the tree. As has been the case with finite-state systems, the automata-theoretic framework is quite versatile. We demonstrate it by solving several versions of the model-checking problem for μ-calculus specifications and prefix-recognizable systems, and by solving the realizability and synthesis problems for μ-calculus specifications with respect to prefix-recognizable environments.
['Orna Kupferman', 'Moshe Y. Vardi']
An automata-theoretic approach to reasoning about infinite-state systems