Splicing systems and the Chomsky hierarchy

TL;DR

This paper investigates the computational properties of splicing systems, establishing their placement within the Chomsky hierarchy and providing decidability results for language equivalence.

Contribution

It proves the decidability of language equality involving splicing systems and shows that alphabetic splicing systems generate context-free languages.

Findings

Decidability of language equality between circular splicing and regular languages.

Alphabetic splicing systems generate context-free languages.

New insights into the placement of splicing languages within the Chomsky hierarchy.

Abstract

In this paper, we prove decidability properties and new results on the position of the family of languages generated by (circular) splicing systems within the Chomsky hierarchy. The two main results of the paper are the following. First, we show that it is decidable, given a circular splicing language and a regular language, whether they are equal. Second, we prove the language generated by an alphabetic splicing system is context-free. Alphabetic splicing systems are a generalization of simple and semi-simple splicin systems already considered in the literature.