Document Open Access Logo

Unambiguisability and Register Minimisation of Min-Plus Models

Authors Shaull Almagor , Guy Arbel , Sarai Sheinvald

PDF

File

Thumbnail PDF
PDF
LIPIcs.ICALP.2026.159.pdf
  • Filesize: 1.09 MB
  • 14 pages

Document Identifiers

Related Versions

Subject Classification

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

Metrics

Abstract

We study the unambiguisability problem for min-plus (tropical) weighted automata (WFAs), and the register-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 for tropical WFAs. Our proof is via reduction to WFA determinisability, which was recently shown to be decidable. To obtain this reduction, we develop a characterisation of unambiguisability via gaps between runs. On the negative side, we show that CRA register minimisation is undecidable already for inputs with 7 registers, and hence also for any larger fixed number of registers.

Cite As Get BibTex

Shaull Almagor, Guy Arbel, and Sarai Sheinvald. Unambiguisability and Register Minimisation of Min-Plus Models. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 159:1-159:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.159

Author Details

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

Funding

  • Almagor, Shaull: ISRAEL SCIENCE FOUNDATION (grant No. 989/22).

References

  1. Shaull Almagor, Guy Arbel, and Sarai Sheinvald. A complexity bound for determinisation of min-plus weighted automata. In 2026 41st Annual Symposium on Logic in Computer Science (LICS), 2026. Google Scholar
  2. Shaull Almagor, Guy Arbel, and Sarai Sheinvald. Determinization of min-plus weighted automata is decidable. In Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 247-257. SIAM, 2026. URL: https://arxiv.org/abs/2503.23826.
  3. Shaull Almagor, Udi Boker, and Orna Kupferman. What’s decidable about weighted automata? Information and Computation, 282:104651, 2020. Special issue on 9th International Workshop Weighted Automata: Theory and Applications (WATA 2018). URL: https://doi.org/10.1016/j.ic.2020.104651.
  4. Shaull Almagor, Michaël Cadilhac, Filip Mazowiecki, and Guillermo A. Pérez. Weak cost register automata are still powerful. Int. J. Found. Comput. Sci., 31(6):689-709, 2020. URL: https://doi.org/10.1142/S0129054120410026.
  5. Rajeev Alur, Loris DAntoni, Jyotirmoy Deshmukh, Mukund Raghothaman, and Yifei Yuan. Regular functions and cost register automata. In 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science, pages 13-22. IEEE, 2013. URL: https://doi.org/10.1109/LICS.2013.65.
  6. Jason P Bell and Daniel Smertnig. Computing the linear hull: Deciding deterministic? and unambiguous? for weighted automata over fields. In 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1-13. IEEE, 2023. URL: https://doi.org/10.1109/LICS56636.2023.10175691.
  7. Yahia Idriss Benalioua, Nathan Lhote, and Pierre-Alain Reynier. Minimizing Cost Register Automata over a Field. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024), volume 306 of Leibniz International Proceedings in Informatics (LIPIcs), pages 23:1-23:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPIcs.MFCS.2024.23.
  8. Ronald Book, Shimon Even, Sheila Greibach, and Gene Ott. Ambiguity in graphs and expressions. IEEE Transactions on Computers, 100(2):149-153, 1971. URL: https://doi.org/10.1109/T-C.1971.223204.
  9. Krishnendu Chatterjee, Laurent Doyen, and Thomas A Henzinger. Quantitative languages. ACM Transactions on Computational Logic (TOCL), 11(4):1-38, 2010. URL: https://doi.org/10.1145/1805950.1805953.
  10. Laure Daviaud. Register complexity and determinisation of max-plus automata. ACM SIGLOG News, 7(2):4-14, 2020. URL: https://doi.org/10.1145/3397619.3397621.
  11. Manfred Droste, Werner Kuich, and Heiko Vogler. Handbook of weighted automata. Springer Science & Business Media, 2009. Google Scholar
  12. Emmanuel Filiot, Ismaël Jecker, Nathan Lhote, Guillermo A Pérez, and Jean-François Raskin. On delay and regret determinization of max-plus automata. In 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1-12. IEEE, 2017. URL: https://doi.org/10.1109/LICS.2017.8005096.
  13. K. Hashiguchi. Limitedness theorem on finite automata with distance functions. Journal of computer and system sciences, 24(2):233-244, 1982. URL: https://doi.org/10.1016/0022-0000(82)90051-4.
  14. K. Hashiguchi. New upper bounds to the limitedness of distance automata. Theoretical Computer Science, 233(1-2):19-32, 2000. URL: https://doi.org/10.1016/S0304-3975(97)00260-0.
  15. Ismaël Jecker, Filip Mazowiecki, and David Purser. Determinisation and unambiguisation of polynomially-ambiguous rational weighted automata. In Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science, pages 1-13, 2024. URL: https://doi.org/10.1145/3661814.3662073.
  16. Daniel Kirsten. Distance desert automata and the star height problem. RAIRO-Theoretical Informatics and Applications, 39(3):455-509, 2005. URL: https://doi.org/10.1051/ITA:2005027.
  17. Daniel Kirsten and Sylvain Lombardy. Deciding unambiguity and sequentiality of polynomially ambiguous min-plus automata. In 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, pages 589-600. IBFI Schloss Dagstuhl, 2009. URL: https://doi.org/10.4230/LIPIcs.STACS.2009.1850.
  18. D. Krob. The equality problem for rational series with multiplicities in the tropical semiring is undecidable. International Journal of Algebra and Computation, 4(3):405-425, 1994. URL: https://doi.org/10.1142/S0218196794000063.
  19. H. Leung and V. Podolskiy. The limitedness problem on distance automata: Hashiguchi’s method revisited. Theoretical Computer Science, 310(1-3):147-158, 2004. URL: https://doi.org/10.1016/S0304-3975(03)00377-3.
  20. Mehryar Mohri. Compact representations by finite-state transducers. In 32nd Annual Meeting of the Association for Computational Linguistics, pages 204-209, 1994. URL: https://doi.org/10.3115/981732.981760.
  21. Mehryar Mohri. Finite-state transducers in language and speech processing. Computational linguistics, 23(2):269-311, 1997. Google Scholar
  22. Azaria Paz. Introduction to probabilistic automata. Academic Press, 2014. Google Scholar
  23. Marcel Paul Schützenberger. On the definition of a family of automata. Inf. Control., 4(2-3):245-270, 1961. URL: https://doi.org/10.1016/S0019-9958(61)80020-X.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact