Generalised sequential crossover of words and languages

TL;DR

This paper introduces a new operation called Generalised Sequential Crossover (GSCO) for words and languages, modeling biological crossover, and explores its properties and relation to regular and sub-regular language classes.

Contribution

The paper defines GSCO for words and languages, analyzes its properties, and compares its language classes with known sub-regular classes, extending the understanding of language operations.

Findings

GSCO* (L) is a subclass of regular languages for any language L

Comparison of GSCO language classes with sub-regular classes

GSCO models biological crossover in a formal language framework

Abstract

In this paper, we propose a new operation, Generalised Sequential Crossover (GSCO) of words, which in some sense an abstract model of crossing over of the chromosomes in the living organisms. We extend GSCO over language $L$ iteratively ($GSCO^*(L)$ as well as iterated GSCO over two languages $GSCO^*(L_1,L_2)$). Our study reveals that $GSCO^*(L)$ is subclass of regular languages for any $L$. We compare the different classes of GSCO languages with the prominent sub-regular classes.