Non-emptiness Test for Automata over Words Indexed by the Reals and Rationals
Résumé
Automata have been defined to recognize languages of words indexed by linear orderings, which generalize the usual notions of finite, infinite, and ordinal words. The reachability problem for these automata has already been solved for scattered linear orderings. In this paper, we design an analogous procedure that solves reachability over the specific domains R and Q. Given an automaton on linear orderings, this procedure decides in polynomial time whether this automaton accepts at least one word indexed by R or by Q. We claim that this algorithm constitutes an essential step to designing effective decision procedures for the first-order monadic theory of order interpreted over R or Q.
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