Pseudo-inversion on formal languages

Abstract

We consider the pseudo-inversion operation inspired by a biological event as a result of the partial inversion. We define the pseudo-inversion of a string w=uxv to consist of all strings vRxuR, where uv ≠ λ and consider the operation from a formal language theoretic viewpoint. We show that regular languages are closed under the pseudo-inversion operation whereas context-free languages are not. Furthermore, we consider the iterated pseudo-inversion operation and establish the basic properties. Finally, we introduce the pseudo-inversion-freeness and examine closure properties and decidability problems for regular and context-free languages. We establish that pseudo-inversion-freeness is decidable in polynomial time for regular languages and undecidable for context-free languages. © 2014 Springer International Publishing Switzerland.