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 significantly simplifies the previous decidability argument and provides a tighter analysis, thus serving as a critical step towards a tight complexity bound.

💡 Research Summary

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The paper addresses the long‑standing open problem of determining the computational complexity of the determinisation problem for min‑plus (tropical) weighted finite automata (WFAs). While recent work