Abstract
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.
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