A note on optimal supervisory control

Supervisors of discrete-event systems are compared. It is shown that if the language generated by the first supervised process is contained in the language generated by the second, and assuming that the language generated by the second process satisfies a certain fairness condition, then the first occurrence time of each event in the second system precedes its occurrence in the first, and the same holds for all its subsequent occurrences. This proves that the supervisor synthesizing the largest language is optimal in the sense that it runs fastest