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A Complexity Bound for Determinisation of Min-Plus Weighted Automata

Authors Shaull Almagor , Guy Arbel , Sarai Sheinvald

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LIPIcs.LICS.2026.5.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Quantitative automata
Keywords
  • Automata
  • Weighted Automata
  • Determinisation
  • Tropical
  • Min Plus
  • Primitive Recursive

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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, showing it is primitive recursive. 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, and Sarai Sheinvald. A Complexity Bound for Determinisation of Min-Plus Weighted Automata. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.LICS.2026.5

Author Details

Shaull Almagor
  • Department of Computer Science, Technion, Haifa, Israel
Guy Arbel
  • Department of Computer Science, Technion, Haifa, Israel
Sarai Sheinvald
  • Department of Computer Science, Technion, Haifa, Israel

Funding

  • Almagor, Shaull: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 989/22).

References

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