Decidable Theories of $\omega$-Layered Metric Temporal Structures
Angelo Montanari, Adriano Peron, Alberto Policriti
Abstract:
This paper focuses on decidability problems for metric and layered temporal
logics which allow one to model time granularity in various contexts. The
decidability of pure metric (nongranular) fragments and of metric temporal
logics endowed with finitely many layers has been already proved by reduction
to the decidability problem of the wellknown theory S1S. In the present work,
we prove the decidability of both the theory of metric temporal structures
provided with an infinite number of arbitrarily coarse temporal layers and the
theory of metric temporal structures provided with an infinite number of
arbitrarily fine temporal layers. The proof for the first theory is obtained
by reduction to the decidability problem of an extension of S1S which is
proved to be the logical counterpart of the class of \omegalanguages accepted
by systolic tree automata. The proof for the second one is done through the
reduction to the monadic secondorder decidable theory of k successors SkS.