Semigroups, Groups and Grammar Inference Problem

In the paper we analyse a problem of inferring a grammar jrom a given sample of a language. We try to present an algebraic formalism capable of describing the issue. We consider two cases: a case of inferring canonical finite-state grammars, and a case of inferring general grammars. In both cases we define a semigroup structure. Finally we look at the possibility of getting a structure of a group.