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Satisfiability of Multivalued Circuits with Lists

Authors Paweł M. Idziak , Piotr Kawałek , Jacek Krzaczkowski , Armin Weiß

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LIPIcs.MFCS.2026.80.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Complexity classes
Keywords
  • satisifiability
  • circuit satisfiability
  • solving equations
  • lists

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Abstract

We study the problem ListCSat of satisfiability of multivalued circuits, whose input values are restricted by lists. We obtain a clear description of quasipolynomial time cases of the problem, where the time complexity is determined by the set of gates which are allowed to build such circuits. That is, algebraic structures induced by gates which allow for a quasipolynomial time algorithm decompose into a direct product L × N, where the polynomial clone of L is isomorphic to the clone of two element lattice and polynomial clone of N is isomorphic to the clone of some finite nilpotent Malcev algebra. If such a decomposition does not exist the ListCSat problem is NP-complete. The result applies to a general setting of finite algebras from congruence modular varieties. In our tractability proofs we assume certain lower bounds for the Boolean CC-circuits. We discuss the cases in which such an assumption can be avoided and polynomial/quasipolynomial time algorithms exist unconditionally.

Cite As Get BibTex

Paweł M. Idziak, Piotr Kawałek, Jacek Krzaczkowski, and Armin Weiß. Satisfiability of Multivalued Circuits with Lists. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 80:1-80:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.80

Author Details

Paweł M. Idziak
  • Jagiellonian University, Kraków, Poland
Piotr Kawałek
  • TU Wien, Austria
Jacek Krzaczkowski
  • University of Maria Curie-Skłodowska, Lublin, Poland
Armin Weiß
  • FMI, Universität Stuttgart, Germany

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.
  • 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.

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