Unambiguisability and Register Minimisation of Min-Plus Models

TL;DR

This paper investigates the decidability of unambiguisability and register minimisation in min-plus models, establishing decidability for WFAs but undecidability for CRAs.

Contribution

It proves that WFA unambiguisability is decidable by reduction to WFA determinisability, and shows CRA counter minimisation is undecidable even with fixed registers.

Findings

WFA unambiguisability is decidable.

CRA counter minimisation is undecidable with 7 registers.

The results resolve a long-standing open problem in the field.

Abstract

We study the unambiguisability problem for min-plus (tropical) weighted automata (WFAs), and the counter-minimisation problem for tropical Cost Register Automata (CRAs), which are expressively-equivalent to WFAs. Both problems ask whether the "amount of nondeterminism" in the model can be reduced. We show that WFA unambiguisability is decidable, thus resolving this long-standing open problem. Our proof is via reduction to WFA determinisability, which was recently shown to be decidable. On the negative side, we show that CRA counter minimisation is undecidable, even for a fixed number of registers (specifically, already for 7 registers).