On the solutions of linear systems over additively idempotent semirings
<|reference_start|>On the solutions of linear systems over additively idempotent semirings: The aim of this article is to solve the system $XA=Y$ where $A=(a_{ij})\in M_{m\times n}(S)$, $Y\in S^{m}$ and $X$ is an unknown vector of size $n$, being $S$ an additively idempotent semiring. If the system has solutions then we completely characterize its maximal one, and in the particular case where $S$ is a generalized tropical semiring a complete characterization of its solutions is provided as well as an explicit bound of the computational cost associated to its computation. Finally, when $S$ is finite, we give a cryptographic application by presenting an attack to the key exchange protocol proposed by Maze, Monico and Rosenthal.<|reference_end|>
@article{sánchez2024on,
    title={On the solutions of linear systems over additively idempotent semirings},
    author={'Alvaro Otero S'anchez, Daniel Camaz'on and Juan Antonio L'opez
  Ramos},
    journal={arXiv preprint arXiv:2404.03294},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.03294},
    primaryClass={cs.IT math.IT math.RA}
}