Word Automata and Time Granularities

Abstract

The relevance of the problem of managing periodic phenomena is widely recognized in different areas of computer science. One of the most effective attempts to manage periodic phenomena takes advantage of the notion of time granularity, which can be thought of as the partitioning of a subset of a temporal domain into groups of elements, where each group is perceived as an indivisible unit (a granule). This chapter provides a detailed account of various automaton-based formalisms that cope with the notion of periodicity and that of time granularity.

We first review the notion of single-string automaton [25], which is a very restricted form of Büchi automaton accepting a single infinite word. Single-string automata provide the first basic formalism for representing and reasoning on ultimately periodic time granularities, that is, temporal structures that, starting from a given point, periodically group instants of the underlying temporal domain.