Automata and temporal logic over arbitrary linear time

Details Automata and temporal logic over arbitrary linear time Automata and temporal logic over arbitrary linear time

2011-01-10

arxiv.org/abs/1101.1731v1

Foundations of Software Technology and Theoretical Computer Science, Kanpur : France (2009)

Computer Science

Logic in Computer Science

Scientific paper

10.4230/LIPIcs.FSTTCS.2009.2313

Linear temporal logic was introduced in order to reason about reactive systems. It is often considered with respect to infinite words, to specify the behaviour of long-running systems. One can consider more general models for linear time, using words indexed by arbitrary linear orderings. We investigate the connections between temporal logic and automata on linear orderings, as introduced by Bruy\`ere and Carton. We provide a doubly exponential procedure to compute from any LTL formula with Until, Since, and the Stavi connectives an automaton that decides whether that formula holds on the input word. In particular, since the emptiness problem for these automata is decidable, this transformation gives a decision procedure for the satisfiability of the logic.

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