Automata and Languages Generalized to omega-Continuous Semirings

Abstract We generalize the following two language- and automata-theoretic results to ω-continuous semirings. • (i) The family of languages accepted by finite automata is the smallest class containing all finite languages and closed under union, product and star (Kleene's Theorem). • (ii) The family of languages accepted by pushdown automata is the family ofcontext-free languages.

[1]  H. Weinert.  Generalized semialgebras over semirings , 1988 .

[2]  Arto Salomaa,et al.  Semirings, Automata, Languages , 1985, EATCS Monographs on Theoretical Computer Science.

[3]  Jacques Sakarovitch.  Kleene's theorem revisited , 1986, IMYCS.

[4]  Jacques Loeckx,et al.  The Foundations of Program Verification , 1987 .

[5]  Werner Kuich,et al.  The Kleene and the Parikh Theorem in Complete Semirings , 1987, ICALP.

[6]  H. Lausch,et al.  Algebra of Polynomials , 1974 .

[7]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

[8]  G. Karner.  On limits in complete semirings , 1992 .