Idefix-Closed Languages and Their Application in Contextual Grammars

TL;DR

This paper explores idefix-closed languages within contextual grammars, comparing their expressive power to other subregular language families, and extends hierarchies by incorporating these new language classes, solving an open problem.

Contribution

It introduces idefix-closed languages into the study of contextual grammars and extends existing hierarchies, also resolving an open problem related to suffix-closed selection languages.

Findings

Extended hierarchies with new language families.

Compared idefix-closed languages to other subregular families.

Solved open problem on internal contextual grammars with suffix-closed languages.

Abstract

In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate infix-, prefix-, and suffix-closed languages (referred to as idefix-closed languages) and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, commutative, circular, union-free, star, and comet languages). Further, we compare the families of the hierarchies obtained for external and internal contextual grammars with the language families defined by these new types for the selection. In this way, we extend the existing hierarchies by new language families. Moreover, we solve an open problem regarding internal contextual grammars with suffix-closed selection languages.