Signed real measure of regular languages

This paper reviews and extends the recent work on signed real measure of regular languages for discrete-event supervisory control within a unified framework. The language measure provides total ordering of any set of partially ordered sublanguages of a regular language to allow quantitative evaluation of the controlled behavior of deterministic finite state automata under different supervisors. The paper presents a procedure by which performance of different supervisors can be evaluated based on a common quantitative tool. Two algorithms are discussed for computation of the language measure. A physical interpretation of the language measure is given from the perspective of discrete-event supervisory control synthesis.