Solving one-sided linear systems over symmetrized and supertropical semiring
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909014389948416 |
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| author | Alhussaini, Sulaiman Sergeev, Sergei |
| author_facet | Alhussaini, Sulaiman Sergeev, Sergei |
| contents | One-sided linear systems of the form ``$Ax=b$'' are well-known and extensively studied over the tropical (max-plus) semiring and wide classes of related idempotent semirings. The usual approach is to first find the greatest solution to such system in polynomial time and then to solve a much harder problem of finding all minimal solutions. We develop an extension of this approach to the same systems over two well-known extensions of the tropical semiring: symmetrized and supertropical, and discuss the implications of our findings for the tropical cryptography. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_03551 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving one-sided linear systems over symmetrized and supertropical semiring Alhussaini, Sulaiman Sergeev, Sergei Rings and Algebras 15A80, 15A06, 94A60 One-sided linear systems of the form ``$Ax=b$'' are well-known and extensively studied over the tropical (max-plus) semiring and wide classes of related idempotent semirings. The usual approach is to first find the greatest solution to such system in polynomial time and then to solve a much harder problem of finding all minimal solutions. We develop an extension of this approach to the same systems over two well-known extensions of the tropical semiring: symmetrized and supertropical, and discuss the implications of our findings for the tropical cryptography. |
| title | Solving one-sided linear systems over symmetrized and supertropical semiring |
| topic | Rings and Algebras 15A80, 15A06, 94A60 |
| url | https://arxiv.org/abs/2605.03551 |