Functional Closure Properties of Finite ℕ-Weighted Automata

Authors Julian Dörfler , Christian Ikenmeyer



PDF
Thumbnail PDF

File

LIPIcs.ICALP.2024.134.pdf
  • Filesize: 0.77 MB
  • 18 pages

Document Identifiers

Author Details

Julian Dörfler
  • Saarland Informatics Campus (SIC), Saarbrücken Graduate School of Computer Science, Saarland University, Germany
Christian Ikenmeyer
  • University of Warwick, Coventry, UK

Cite As Get BibTex

Julian Dörfler and Christian Ikenmeyer. Functional Closure Properties of Finite ℕ-Weighted Automata. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 134:1-134:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ICALP.2024.134

Abstract

We determine all functional closure properties of finite ℕ-weighted automata, even all multivariate ones, and in particular all multivariate polynomials. We also determine all univariate closure properties in the promise setting, and all multivariate closure properties under certain assumptions on the promise, in particular we determine all multivariate closure properties where the output vector lies on a monotone algebraic graph variety.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata extensions
Keywords
  • Finite automata
  • weighted automata
  • counting
  • closure properties
  • algebraic varieties

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Rudolf Ahlswede and David E Daykin. An inequality for the weights of two families of sets, their unions and intersections. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 43:183-185, 1978. Google Scholar
  2. Noga Alon and Joel H. Spencer. The Probabilistic Method, Third Edition. Wiley-Interscience series in discrete mathematics and optimization. Wiley, 2008. Google Scholar
  3. Edwin F Beckenbach and Richard Bellman. Inequalities. Springer, Berlin, 1961. Google Scholar
  4. Richard Beigel. Closure properties of GapP and #P. In Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems, pages 144-146. IEEE, 1997. URL: https://doi.org/10.1109/ISTCS.1997.595166.
  5. Swee Hong Chan and Igor Pak. Computational complexity of counting coincidences. CoRR, abs/2308.10214, 2023. URL: https://doi.org/10.48550/arXiv.2308.10214.
  6. Swee Hong Chan and Igor Pak. Equality cases of the alexandrov-fenchel inequality are not in the polynomial hierarchy. CoRR, abs/2309.05764, 2023. URL: https://doi.org/10.48550/arXiv.2309.05764.
  7. David A. Cox, John Little, and Donal O'Shea. Ideals, varieties, and algorithms - An introduction to computational algebraic geometry and commutative algebra (2. ed.). Undergraduate texts in mathematics. Springer, 1997. Google Scholar
  8. Manfred Droste, Werner Kuich, and Heiko Vogler. Handbook of weighted automata. Springer Science & Business Media, 2009. Google Scholar
  9. Manfred Droste and Dietrich Kuske. Weighted automata. In Jean-Éric Pin, editor, Handbook of Automata Theory, pages 113-150. European Mathematical Society Publishing House, Zürich, Switzerland, 2021. URL: https://doi.org/10.4171/Automata-1/4.
  10. HG Hardy, JE Littlewood, and G. Pólya. Inequalities. Cambridge University Press, 1952. Google Scholar
  11. Ulrich Hertrampf, Heribert Vollmer, and Klaus W Wagner. On the power of number-theoretic operations with respect to counting. In Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference, pages 299-314. IEEE, 1995. URL: https://doi.org/10.1109/SCT.1995.514868.
  12. Christian Ikenmeyer and Igor Pak. What is in #P and what is not? In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), pages 860-871. IEEE, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00087.
  13. Christian Ikenmeyer, Igor Pak, and Greta Panova. Positivity of the symmetric group characters is as hard as the polynomial time hierarchy. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 3573-3586. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.ch136.
  14. Ines Klimann, Sylvain Lombardy, Jean Mairesse, and Christophe Prieur. Deciding unambiguity and sequentiality from a finitely ambiguous max-plus automaton. Theoretical Computer Science, 327(3):349-373, 2004. URL: https://doi.org/10.1016/j.tcs.2004.02.049.
  15. Igor Pak. Complexity problems in enumerative combinatorics. In Proceedings of the International Congress of Mathematicians: Rio de Janeiro 2018, pages 3153-3180. World Scientific, 2018. Google Scholar
  16. Igor Pak. Combinatorial inequalities. Notices of the AMS, 66(7), August 2019. Google Scholar
  17. Igor Pak. What is a combinatorial interpretation? to appear: Proc. Open Problems in Algebraic Combinatorics. https://www.samuelfhopkins.com/OPAC/files/proceedings/pak.pdf, 2022.
  18. J Peterson. Beviser for wilsons og fermats theoremer. Tidsskrift for mathematik, 2:64-65, 1872. Google Scholar
  19. 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.
  20. Igor R Shafarevich. Basic algebraic geometry 1: Varieties in projective space. Springer Science & Business Media, 3 edition, 2013. Google Scholar
  21. Michael Spivey. The Chu-Vandermonde identity via Leibniz’s identity for derivatives. The College Mathematics Journal, 47(3):219-220, 2016. Google Scholar
  22. Richard P Stanley. Positivity problems and conjectures in algebraic combinatorics. Mathematics: frontiers and perspectives, 295:319, 1999. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail