Deciding Unambiguity and Sequentiality starting from a Finitely Ambiguous Max-Plus Automaton

TL;DR

This paper establishes the decidability of whether a finitely ambiguous max-plus automaton's recognized series is unambiguous or sequential, providing insights into the hierarchy of max-plus series based on ambiguity.

Contribution

It introduces an effective method to decide unambiguity and sequentiality in finitely ambiguous max-plus automata, advancing understanding of their structural properties.

Findings

Decidability of unambiguity and sequentiality in finitely ambiguous max-plus automata

Hierarchy of max-plus series based on ambiguity levels

Illustrative examples of ambiguity hierarchy

Abstract

Finite automata with weights in the max-plus semiring are considered. The main result is: it is decidable in an effective way whether a series that is recognized by a finitely ambiguous max-plus automaton is unambiguous, or is sequential. A collection of examples is given to illustrate the hierarchy of max-plus series with respect to ambiguity.