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

Automata and temporal logic over arbitrary linear time