Towards Compact and Tractable Automaton-Based Representations of Time Granularities

Different approaches to time granularity have been proposed in the database literature to formalize the notion of calendar, based on algebraic, logical, and string-based formalisms. In this paper, we further develop an alternative approach based on automata, originally proposed in [4], which makes it possible to deal with infinite time granularities in an effective (and efficient) way. In particular, such an approach provides an effective solution to fundamental problems such as equivalence and conversion of time granularities. We focus our attention on two kinds of optimization problems for automaton-based representations, namely, computing the smallest representation and computing the most tractable representation, that is, the one on which crucial algorithms (e.g., granule conversion algorithms) run fastest. We first introduce and compare these two minimization problems; then, we give a polynomial time algorithm that solves the latter.