Signed real measure of regular languages for discrete event supervisory control

This paper reviews, expands, and clarifies the underlying concepts of a signed real measure of regular languages, which has been used as a novel tool for synthesis of discrete event supervisory control systems. The language measure is constructed upon the principles of automata theory and real analysis. It allows total ordering of a set of partially ordered sublanguages of a regular language for quantitative evaluation of the supervised behaviour of deterministic finite state automata (DFSA) under different supervisors. In the setting of the language measure, a supervisor's performance is superior if the supervised plant is more likely to terminate at a good marked state and/or less likely to terminate at a bad marked state. The computational complexity of the language measure algorithm is polynomial in the number of DFSA states.