A Survey of the Theory of Min-Max Systems

Min-max systems are discrete event systems whose timing involves the maximum, minimum, and addition operations. In recent years, progresses have been made in such topics as cycle time computation, ultimate periodicity of trajectories, structural properties, cycle time assignment, etc. They are surveyed in this paper. Furthermore, as an attempt to open new directions for further research we propose two new models referred to as and-or net and and-or event graph. It is found that timed and-or event graphs can be algebraically described by min-max systems. We hope that these new models would accommodate more new results.