Various Types of Comet Languages and their Application in External Contextual Grammars
Marvin Ködding, Bianca Truthe
TL;DR
The paper studies comet-like languages generated by external contextual grammars with selection restricted to subregular language families, and places them into an expanded hierarchy of subregular languages. It derives normal forms for two-sided comet languages, showing every language in $2COM$ can be written as $L = E G^* H$ with $E$ finite and $G \neq \{\emptyset, {\lambda}\}$, and proves that infinite two-sided comet languages admit finite unions of such forms. It establishes that $EC(REG) = EC(LCOM) = EC(RCOM) = EC(2COM)$ and maps a detailed inclusion and incomparability structure among MON, STAR, UF, SYDEF, LCOM, RCOM, 2COM, and related EC families, including several new results. The work clarifies the expressive power of external contextual grammars with restricted selection and provides a foundation for extending hierarchies to additional language families and grammars such as prefix/infix-definite-like and tree-based variants.
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 various comet-like types of languages and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, suffix-closed, commutative, circular, or union-free languages). Further, we compare the language families defined by these types for the selection with each other and with the families of the hierarchy obtained for external contextual grammars. In this way, we extend the existing hierarchy by new language families.