Fixed zeros in the model matching problem for systems over a semiring

This paper studies "fixed zeros" of solutions to the model matching problem for systems over a semiring. Such systems have been used to model queueing systems, communication networks, and manufacturing systems. The main contribution of this paper is the discovery of two fixed zero semimodules, which possess a connection with the extended zero semimodules of solutions to the model matching problem. Intuitively, the fixed zero semimodule provides an essential component that is obtained from the solutions to the model matching problem. For discrete event dynamic systems modeled in max-plus algebra, a common Petri net component constructed from the solutions to the model matching problem can be discovered from the fixed zero structure.