Tech Reports

ULCS-06-001

Is there a future for deductive temporal verification?

Clare Dixon, Michael Fisher and Boris Konev

Abstract

In this paper, we consider a tractable sub-class of propositional linear time temporal logic, and provide a complete clausal resolution calculus for it. The fragment is important as it captures simple Buchi automata. We also show that, just as the emptiness check for a Buchi automaton is tractable, the complexity of deciding unsatisfiability, via resolution, of our logic is polynomial (rather than exponential). Consequently, a Buchi automaton can be represented within our logic, and its emptiness can be tractably decided via deductive methods. This may have a significant impact upon approaches to verification, since techniques such as model checking inherently depend on the ability to check emptiness of an appropriate Buchi automaton. Thus, we also discuss how such a logic might form the basis for practical deductive temporal verification.

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