Unambiguisability and Register Minimisation of Min-Plus Models

Shaull Almagor; Guy Arbel; Sarai Sheinvald

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arXiv · 2512.09484

Unambiguisability and Register Minimisation of Min-Plus Models

Shaull Almagor·Guy Arbel·Sarai Sheinvald

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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).

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Shaull Almagor, Guy Arbel, Sarai Sheinvald. 2025-12-10. Unambiguisability and Register Minimisation of Min-Plus Models. https://arxiv.org/abs/2512.09484

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