A note on the Sylvester equation over max-plus algebra

TL;DR

This paper presents a more precise computational complexity analysis and a succinct representation of the principal solution for the Sylvester equation over max-plus algebra, enhancing understanding of its solvability.

Contribution

It introduces a more accurate complexity measure and a concise form for the principal solution of the Sylvester equation in max-plus algebra.

Findings

Polynomial-time solvability verification via principal solution

Succinct representation of the principal solution

Improved computational complexity understanding

Abstract

It is known that the solvability of a Sylvester equation over max-plus algebra can be determined in polynomial time by verifying its principal solution. A succinct representation of the principal solution is presented, with a more accurate computational complexity, for a Sylvester equation over max-plus algebra.