A Complexity Bound for Determinisation of Min-Plus Weighted Automata

2026-02-01

AI Summary

The determinization problem for minimal weighted automata has long lacked a known complexity upper bound. This work establishes, for the first time, an upper bound on the complexity of this problem within the fast-growing hierarchy and introduces a constructive runtime analysis framework. The proposed framework not only substantially simplifies prior decidability proofs but also enhances the tightness of the analysis, thereby laying a crucial theoretical foundation for future research in this area.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Planning, Routing, and Scheduling: Deterministic Planning

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• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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

Problem

• min-plus weighted automata
• determinisation
• complexity bound
• tropical automata
• Fast-growing hierarchy

Innovation

• min-plus weighted automata
• determinisation
• complexity bound
• Fast-growing hierarchy
• constructive analysis