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arXiv · 2311.02416

Expressive Power of Hypergraph Lambek Grammars

Tikhon Pshenitsyn
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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.

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Tikhon Pshenitsyn. 2023-11-04. Expressive Power of Hypergraph Lambek Grammars. https://arxiv.org/abs/2311.02416

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