Parallel Hyperedge Replacement Grammars

TL;DR

This paper introduces parallel hyperedge replacement grammars, a new language class that encompasses multiple context-free and ET0L languages, and explores their closure properties and potential for formal language hierarchy analysis.

Contribution

It defines parallel hyperedge replacement grammars, demonstrates their synchronization capabilities, and establishes foundational closure results for these languages.

Findings

Parallel hyperedge replacement grammars can be synchronized.

They include all multiple context-free and ET0L languages.

The paper lays groundwork for analyzing hypergraph language hierarchies.

Abstract

In 2018, it was shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is still an open problem as to where to precisely place the word problems of hyperbolic groups in the formal language hierarchy. Motivated by this, we introduce a new language class, the parallel hyperedge replacement string languages, containing all multiple context-free and ET0L languages. We show that parallel hyperedge replacement grammars can be "synchronised", which allows us to establish many useful formal language closure results relating to both the hypergraph and string languages generated by various families of parallel hyperedge replacement grammars, laying the foundations for future work in this area.