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arXiv · 2602.01221

A Complexity Bound for Determinisation of Min-Plus Weighted Automata

Shaull Almagor·Guy Arbel·Sarai Sheinvald
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Abstract

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.

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Shaull Almagor, Guy Arbel, Sarai Sheinvald. 2026-02-01. A Complexity Bound for Determinisation of Min-Plus Weighted Automata. https://arxiv.org/abs/2602.01221

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