Universal First-Order Quantification over Automata
Résumé
Deciding formulas that mix arithmetic and uninterpreted predicates is of practical interest, notably for applications in verication. Some decision procedures consist in building by structural induction an automaton that recognizes the set of models of the formula under analysis, and then testing whether this automaton accepts a non-empty language. A drawback is that universal quantication is usually handled by a reduction to existential quantication and complementation. For logical formalisms in which models are encoded as innite words, this hinders the practical use of this method due to the diculty of complementing innite-word automata. The contribution of this paper is to introduce an algorithm for directly computing the eect of universal rst-order quantiers on automata recognizing sets of models, for formulas involving natural numbers encoded in unary notation. This paves the way to implementable decision procedures for various arithmetic theories.
Domaines
Informatique [cs]
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