arXiv subjects

Guy Arbel

Publications and source records attributed to Guy Arbel.

3 recordsLinked to original sources

arXiv2026

A Complexity Bound for Determinisation of Min-Plus Weighted Automata

The determinisation problem for min-plus (tropical) weighted automata was recently shown to be decidable. However, the proof is purely existential, relying on several non-constructive arguments. Our contribution in this work is twofold: first, we present the first complexity bound for this problem, placing it in the Fast-growing hierarchy. Second, our techniques introduce a versatile framework to analyse runs of weighted automata in a constructive manner. In particular, this simplifies the previous decidability argument and provides a tighter analysis, thus serving as a critical step towards a tight complexity bound.

cs.FL↗

arXiv2025

Unambiguisability and Register Minimisation of Min-Plus Models

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).

cs.FL↗

arXiv2025

Determinization of Min-Plus Weighted Automata is Decidable

We show that the determinization problem for min-plus (tropical) weighted automata is decidable, thus resolving this long-standing open problem. In doing so, we develop a new toolbox for analyzing and reasoning about the run-structure of nondeterministic automata.

cs.FL↗