Transformation of Turing Machines into Context-Dependent Fusion Grammars

TL;DR

This paper demonstrates that context-dependent fusion grammars, which generate hypergraph languages with context restrictions, are computationally universal by transforming Turing machines into these grammars.

Contribution

It introduces a method to transform Turing machines into context-dependent fusion grammars, proving their universality in generating all recursively enumerable languages.

Findings

Turing machines can be simulated by context-dependent fusion grammars

These grammars can generate all recursively enumerable string languages

The transformation preserves language recognition and generation capabilities

Abstract

Context-dependent fusion grammars were recently introduced as devices for the generation of hypergraph languages. In this paper, we show that this new type of hypergraph grammars, where the application of fusion rules is restricted by positive and negative context conditions, is a universal computation model. Our main result is that Turing machines can be transformed into these grammars such that the recognized language of the Turing machine and the generated language of the corresponding context-dependent fusion grammar coincide up to representation of strings as graphs. As a corollary we get that context-dependent fusion grammars can generate all recursively enumerable string languages.