A language measure for discrete-event automata

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Scopus citations


This paper presents the concept and formulation of a signed real measure of regular languages for analysis of discrete-event supervisory control systems. The measure is constructed based upon the principles of language theory and real analysis for quantitative evaluation and comparison of the controlled behavior for discrete-event automata. The marked (i.e., accepted) states of finite-state automata are classified in different categories such that the event strings leading to good and bad marked states have positive and negative measures, respectively. In this setting, a controlled language attempts to disable as many bad strings as possible and as few good strings as possible. Different supervisors may achieve this goal in different ways and generate a partially ordered set of controlled languages. The language measure creates a total ordering on the performance of the controlled languages, which provides a precise quantitative comparison of the controlled plant behavior under different supervisors. The total variation of this language measure induces a norm on the vector space of sublanguages of the given regular language over the Galois field GF(2).

Original languageEnglish (US)
Title of host publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
EditorsGabriel Ferrate, Eduardo F. Camacho, Luis Basanez, Juan. A. de la Puente
PublisherIFAC Secretariat
Number of pages6
ISBN (Print)9783902661746
StatePublished - Jan 1 2002
Event15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain
Duration: Jul 21 2002Jul 26 2002

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
ISSN (Print)1474-6670


Other15th World Congress of the International Federation of Automatic Control, 2002

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

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    Ray, A., & Phoha, S. (2002). A language measure for discrete-event automata. In G. Ferrate, E. F. Camacho, L. Basanez, & J. A. de la Puente (Eds.), IFAC Proceedings Volumes (IFAC-PapersOnline) (1 ed., pp. 181-186). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 15, No. 1). IFAC Secretariat. https://doi.org/10.3182/20020721-6-es-1901.00518