On language decompositions and primality

Abstract

Concatenation of strings and languages is a fundamental operation on formal languages. Here we consider the inverse operation of language decomposition, where we want to represent a given language as a non-trivial concatenation of two languages. The associated notions of prime languages and prime decompositions have been originally introduced by Mateescu, A. Salomaa and Yu. We consider also extensions of the decomposability problem with respect to orthogonal concatenation, as well as, more general operations defined by sets of trajectories. © 2011 Springer-Verlag Berlin Heidelberg.