Expressive Power of Hypergraph Lambek Grammars
Formal Languages and Automata Theory
2023-11-30 v2
Abstract
Hypergraph Lambek grammars (HL-grammars) is a novel logical approach to generating graph languages based on the hypergraph Lambek calculus. In this paper, we establish a precise relation between HL-grammars and hypergraph grammars based on the double pushout (DPO) approach: we prove that HL-grammars generate the same class of languages as DPO grammars with the linear restriction on lengths of derivations. This can be viewed as a complete description of the expressive power of HL-grammars and also as an analogue of the Pentus theorem, which states that Lambek grammars generate the same class of languages as context-free grammars. As a corollary, we prove that HL-grammars subsume contextual hyperedge replacement grammars.
Cite
@article{arxiv.2311.02416,
title = {Expressive Power of Hypergraph Lambek Grammars},
author = {Tikhon Pshenitsyn},
journal= {arXiv preprint arXiv:2311.02416},
year = {2023}
}