Equations over Finite Monoids with Infinite Promises
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911645090971648 |
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| author | Larrauri, Alberto Mottet, Antoine Živný, Stanislav |
| author_facet | Larrauri, Alberto Mottet, Antoine Živný, Stanislav |
| contents | Larrauri and Živný [ICALP'25/ACM ToCL'24] recently established a complete complexity classification of the problem of solving a system of equations over a monoid $N$ assuming that a solution exists over a monoid $M$, where both monoids are finite and $M$ admits a homomorphism to $N$. Using the algebraic approach to promise constraint satisfaction problems, we extend their complexity classification in two directions: we obtain a complexity dichotomy in the case where arbitrary relations are added to the monoids, and we moreover allow the monoid $M$ to be finitely generated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equations over Finite Monoids with Infinite Promises Larrauri, Alberto Mottet, Antoine Živný, Stanislav Computational Complexity Larrauri and Živný [ICALP'25/ACM ToCL'24] recently established a complete complexity classification of the problem of solving a system of equations over a monoid $N$ assuming that a solution exists over a monoid $M$, where both monoids are finite and $M$ admits a homomorphism to $N$. Using the algebraic approach to promise constraint satisfaction problems, we extend their complexity classification in two directions: we obtain a complexity dichotomy in the case where arbitrary relations are added to the monoids, and we moreover allow the monoid $M$ to be finitely generated. |
| title | Equations over Finite Monoids with Infinite Promises |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2502.06762 |