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Article Dans Une Revue Journal of Computer and System Sciences Année : 1993

On the expressive power of temporal logic for finite words

Résumé

We study the expressive power of linear propositional temporal logic interpreted on finite sequences or words. We first give a transparent proof of the fact that a formal language is expressible in this logic if and only if its syntactic semigroup is finite and aperiodic. This gives an effective algorithm to decide whether a given rational language is expressible. Our main result states a similar condition for the "restricted" temporal logic (RTL), obtained by discarding the until operator. A formal language is RTL-expressible if and only if its syntactic semigroup is finite and satisfies a certain simple algebraic condition. This leads to a polynomial time algorithm to check whether the formal language accepted by an n-state deterministic automaton is RTL-expressible.
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Dates et versions

hal-00020069 , version 1 (04-03-2006)

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Joelle Cohen, Dominique Perrin, Jean-Eric Pin. On the expressive power of temporal logic for finite words. Journal of Computer and System Sciences, 1993, 46, pp.271-294. ⟨10.1016/0022-0000(93)90005-H⟩. ⟨hal-00020069⟩
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