Unambiguisability and Register Minimisation of Min-Plus Models
Formal Languages and Automata Theory
2026-04-30 v2
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).
Keywords
Cite
@article{arxiv.2512.09484,
title = {Unambiguisability and Register Minimisation of Min-Plus Models},
author = {Shaull Almagor and Guy Arbel and Sarai Sheinvald},
journal= {arXiv preprint arXiv:2512.09484},
year = {2026}
}