Signed real measure of regular languages

This chapter formulates a signed real measure of sublanguages of a regular language based on the principles of automata theory and real analysis. The measure allows total ordering of a set of partially ordered sublanguages of the regular language for quantitative evaluation of the controlled behavior 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.