Unambiguous automata denoting finitely sequential functions

Abstract

The min-plus automata with real weights are interesting both in theory and in practice, e.g. their variants are used as a data structure in speech recognition. In this paper we study automata which are finite unions of deterministic ones, called finitely sequential automata. Such automata allow fast detection of optimal paths in parallel while still allowing to express ambiguous functions. We provide a polynomial time algorithm which decides if the given min-plus unambiguous automaton, with rational weights, has a finitely sequential version and we show how to build such equivalent one if the answer is positive. To this end, we introduce the Fork Property which plays the same role as the negation of the Twin Property in case of determinisation. We show that an unambiguous automaton can be transformed into a finitely sequential one if and only if the Fork Property is not satisfied. © 2013 Springer-Verlag Berlin Heidelberg.