Star-Connected Flat Languages and Automata

Issue title: SPECIAL ISSUE ON CONCURRENCY SPECIFICATION AND PROGRAMMING (CS&P 2005) Ruciane-Nide, Poland, 28–30 September 2005

Article type: Research Article

Authors: Klunder, Barbara

Affiliations: Faculty of Mathematics and Computer Science Nicolaus Copernicus University Toruń, Poland. E-mail: klunder@mat.uni.torun.pl

Abstract: Star-connected rational expressions were considered only as expressions defining trace languages. In this paper we continue the study of the class of flat languages defined by this kind of rational expressions. We strengthen results of [4] and prove that any star-connected language has an automaton with cycles which are composition of connected cycles. This condition is sufficient for star-connected languages provided that the dependency relation is transitive. As a consequence we obtain for every alphabet stronger pumping lemma for star-connected languages. Finally, the product of two automata inherits this property from the components and thus for alphabet with transitive dependency relation the set of all star-connected languages is closed under intersections.

Keywords: trace language, star-connected rational expressions, finite automata

Journal: Fundamenta Informaticae, vol. 72, no. 1-3, pp. 235-243, 2006