# Specifying timed state sequences in powerful decidable logics and timed automata

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## Abstract

A monadic second-order language, denoted by \(\mathcal{L}d\), is introduced for the specification of sets of timed state sequences. A fragment of \(\mathcal{L}d\), denoted by , is proved to be expressively complete for timed automata (Alur and Dill), i.e., every timed regular language is definable by a -formula and every -formula defines a timed regular language. As a consequence the satisfiability problem for is decidable.

Timed temporal logics are shown to be effectively embeddable into and hence turn out to have a decidable theory. This applies to TL

_{Г}(Manna and Pnueli) and EMITL_{p}, which is obtained by extending the logic MITL_{p}(Alur and Henzinger) by automata operators (Sistla, Vardi, and Wolper).For every positive natural number

*k*the full monadic second-order logic \(\mathcal{L}d\) and are equally expressive modulo the set of timed state sequences of variability ≤*k*. Therefore the \(\mathcal{L}d\)-theory of the set of timed state sequences of variability ≤*k*is decidable.## Keywords

Regular Language Satisfiability Problem Time Automaton Distance Formula Infinite Word
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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