Solving Promise Equations over Monoids and Groups

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.

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Journal
ACM Transactions on Computational Logic
Published
2024-09-27
DOI
https://doi.org/10.1145/3698106
Primary Topic
Advanced Graph Theory Research
Type
article
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article

Solving Promise Equations over Monoids and Groups

Alberto Larrauri, Stanislav Živný
ACM Transactions on Computational Logic
Advanced Graph Theory Research
article

Solving Promise Equations over Monoids and Groups

Alberto Larrauri, Stanislav Živný
article en

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.

ACM Transactions on Computational LogicVol. 26(1)
University of Oxford (GB)
Openalex Percentile: Top 80%
Advanced Graph Theory Research
DOISourceOpenAlex
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Solving Promise Equations over Monoids and Groups — Alberto Larrauri, Stanislav Živný · ACM Transactions on Computational Logic (2024) | TGRS Research Map | TGRS