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Circuit Equivalence in 2-Nilpotent Algebras

Authors Piotr Kawałek , Michael Kompatscher , Jacek Krzaczkowski

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Author Details

Piotr Kawałek
  • Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Austria
  • Institute of Computer Science, University of Maria Curie-Skłodowska, Lublin, Poland
Michael Kompatscher
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Jacek Krzaczkowski
  • Institute of Computer Science, University of Maria Curie-Skłodowska, Lublin, Poland

Funding

  • Kawałek, Piotr: Funded by the European Union (ERC, POCOCOP, 101071674). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. This research was funded in whole or in part by National Science Centre, Poland #2021/41/N/ST6/ 03907. For the purpose of Open Access, the author has applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.
  • Kompatscher, Michael: This work has been supported by projects PRIMUS/24/SCI/008 and UNCE/SCI/022 of Charles University.
  • Krzaczkowski, Jacek: This research was funded in whole or in part by National Science Centre, Poland #2022/45/B/ST6/02229. For the purpose of Open Access, the author has applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.

Acknowledgements

We would like to thank Prof. Paweł Idziak for bringing us together in the spring of 2018 (by inviting the second author to Kraków), which ultimately lead to this publication.

Cite As Get BibTex

Piotr Kawałek, Michael Kompatscher, and Jacek Krzaczkowski. Circuit Equivalence in 2-Nilpotent Algebras. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 45:1-45:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.STACS.2024.45

Abstract

The circuit equivalence problem Ceqv(A) of a finite algebra A is the problem of deciding whether two circuits over A compute the same function or not. This problem not only generalises the equivalence problem for Boolean circuits, but is also of interest in universal algebra, as it models the problem of checking identities in A. In this paper we prove that Ceqv(A) ∈ 𝖯, if A is a finite 2-nilpotent algebra from a congruence modular variety.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Complexity classes
Keywords
  • circuit equivalence
  • identity checking
  • nilpotent algebra

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