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Measure of regular languages

Surana A., Ray A.

Demonstratio Mathematica

2004

Vol. 37, nr 2

485--503

This paper reviews and extends the recent work on signed real measure of regular languages within a unified framework. The language measure provides total ordering of partially ordered sets of 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 provided for computation of the language measure and their equivalence is established along with a physical interpretation from the probabilistic perspective.