On languages generated by semigroups

Abstract

In this paper we investigate properties of classes of languages generated by semigroups in the following sense: Let S be a semigroup, s its element, A an alphabet and f a mapping which assignes to each a ε A a finite subset f(a) of S. A word w=a1.. an ε A+ belongs to the language generated by S, f, s and A iff the following condition holds: We investigate the languages generated in this sense by certain types of semigroups. It is important to emphasize that we do not consider the empty word, thus all languages are subsets of free semigroups of the form A+, similarly all homomorphisms we investigate are semigroup homomorphisms only. Since the proofs of our results are based on rather complicated semigroup constructions we sketch them out or omit at all. The detailed proofs are to be presented in [10].