Affiliation:
1. Faculty of Informatics, Eötvös Loránd University, P.O.B. 120, 1518 Budapest, Hungary
2. Inst. of Informatics, University of Szeged, P.O.B. 652, 6701 Szeged, Hungary
Abstract
A bisemigroup is a set with two associative operations. Subsets of free bisemigroups are called bisemigroup languages. Recognizable, regular and MSO-definable bisemigroup languages have been studied earlier, and these classes are known to be equal. In this paper we prove a Kleene theorem for bisemigroup languages, namely we show that the class of recognizable bisemigroup languages is the least class which contains the finite languages and closed under the operations of union, horizontal and vertical product, horizontal and vertical iteration, ξ-substitution and a restricted version of the the ξ-iteration. We extend our result to binoid languages, i.e., to subsets of free algebras, where the two associative operations share a common identity element.
Publisher
World Scientific Pub Co Pte Lt
Subject
Computer Science (miscellaneous)
Reference11 articles.
1. M. Bojańczyk and I. Walukiewicz, Logic and Automata: History and Perspectives, eds. J. Flum, E. Grädel and Th. Wilke (Amsterdam University Press, 2008) pp. 107–132.
2. A note on identities of two-dimensional languages
3. Axiomatizing the identities of binoid languages