A complex measure of non-regular languages for discrete-event supervisory control

The measure of regular languages, recently introduced in technical literature, has been the driving force for quantitative analysis and synthesis of discrete-event supervisory (DES) control systems dealing with finite state automata (equivalently, regular languages). This paper extends the signed real measure of regular languages, to a complex measure of non-regular languages, generated by linear context free grammars; the concept is illustrated by an example. The complex measure becomes equivalent to the signed real measure if the linear context free grammar is degenerated to a regular grammar.