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Solving Promise Equations over Monoids and Groups

Authors Alberto Larrauri , Stanislav Živný

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Author Details

Alberto Larrauri
  • Department of Computer Science, University of Oxford, UK
Stanislav Živný
  • Department of Computer Science, University of Oxford, UK

Funding

This research was funded in whole by UKRI EP/X024431/1. For the purpose of Open Access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. All data is provided in full in the results section of this paper.

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Alberto Larrauri and Stanislav Živný. Solving Promise Equations over Monoids and Groups. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 146:1-146:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.146

Abstract

We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity classification for the same problem over groups.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Constraint and logic programming
Keywords
  • constraint satisfaction
  • promise constraint satisfaction
  • equations
  • minions

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