Matrix Graph Grammars: Transformation of Restrictions

TL;DR

This paper advances the Matrix Graph Grammars framework by enabling the translation and movement of application conditions within rule sequences, facilitating multidigraph rewriting.

Contribution

It introduces methods for translating post-conditions to pre-conditions and delocalizing application conditions within sequences, expanding the framework's capabilities.

Findings

Enables multidigraph rewriting using application conditions.

Provides techniques for translating and delocalizing restrictions.

Enhances analysis of rule applicability and independence.

Abstract

In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operations only. In previous works, we developed analysis techniques enabling the study of the applicability of rule sequences, their independence, stated reachability and the minimal digraph able to fire a sequence. In [20], graph constraints and application conditions (so-called restrictions) have been studied in detail. In the present contribution we tackle the problem of translating post-conditions into pre-conditions and vice versa. Moreover, we shall see that application conditions can be moved along productions inside a sequence (restriction delocalization). As a practical-theoretical application we show how application conditions allow us to perform multidigraph rewriting (as opposed to simple digraph rewriting) using Matrix Graph Grammars