Application of Generalised sequential crossover of languages to generalised splicing

TL;DR

This paper explores the application of generalized sequential crossover operations to study generalized splicing languages, demonstrating that certain subclasses of these languages are always regular, thus advancing formal language theory.

Contribution

It introduces an application of iterated generalized sequential crossover to generalized splicing, proving regularity of specific subclasses of these languages.

Findings

The subclass $GS(X,Y, ext{FIN})$ is always regular.

Generalized sequential crossover can be applied to analyze generalized splicing.

Certain language classes maintain regularity under this operation.

Abstract

This paper outlines an application of iterated version of generalised sequential crossover of two languages (which in some sense, an abstraction of the crossover of chromosomes in living organisms) in studying some classes of the newly proposed generalised splicing ($GS$) over two languages. It is proved that, for $X,Y \in \{FIN, REG, LIN, CF, CS, RE \}, \sg \in FIN$, the subclass of generalized splicing languages namely $GS(X,Y,\sg)$, (which is a subclass of the class $GS(X,Y,FIN)$) is always regular.