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arXiv · 2605.03551

Solving one-sided linear systems over symmetrized and supertropical semiring

Sulaiman Alhussaini·Sergei Sergeev
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Abstract

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.

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Sulaiman Alhussaini, Sergei Sergeev. 2026-05-05. Solving one-sided linear systems over symmetrized and supertropical semiring. https://doi.org/10.1016/j.laa.2026.04.009

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