We continue here the development of our description of the pullback approach to graph rewriting-already shown to encompass both the NCE and the double-pushout approach, by describing parallel application of rewriting rules. We show that this new framework provides a genuine deenition of parallel rewriting (parallel application of several rewriting rules at several diierent places in the graph i...

We define transactional graph transformation systems (t-gtss), a mild extension of the ordinary framework for the double-pushout approach to graph transformation, which allows to model transactional activities. Generalising the work on zero-safe nets, the new graphical formalism is based on a typing discipline which induces a distinction between stable and unstable items. A transaction is then ...

The goal of this chapter is to discuss pushouts in the category of algebraic spaces. This can be done with varying assumptions. A fairly general pushout construction is given in [TT13]: one of the morphisms is affine and the other is a closed immersion. We discuss a particular case of this in Section 2 where we assume one of the morphisms is affine and the other is a thickening, a situation tha...

Grammatica is a prototype implementation of algebraic graph transformation based on relation algebra. It has been implemented using Mathematica on top of the Combinatorica package, and runs therefore on most platforms. It consists of Mathematica routines for representing, manipulating, displaying and transforming graphs, as well as routines implementing some relation algebra-theoretic operation...

We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H,G,α, β) is deformed using a combinatorial datum (σ, v, r) consisting of an automorphism σ of H , a permutation v of the set G and a transition map r : G → H in order to obtain a new matched pair `

A single pushout approach to the transformation of attributed partial graphs based on categories of partial algebras and partial mor-phisms is introduced. A suucient condition for pushouts in these categories is presented. As the synchronization mechanism we use amalgamation of rules and show how synchronization can be minimized. We point out how the results obtained can be employed in order to...

0AHU The goal of this chapter is to discuss pushouts in the category of algebraic spaces. This can be done with varying assumptions. A fairly general pushout construction is given in [TT13]: one of the morphisms is affine and the other is a closed immersion. We discuss a particular case of this in Section 2 where we assume one of the morphisms is affine and the other is a thickening, a situatio...

Hierarchically distributed graph transformation ooers means to model diierent aspects of open distributed systems very intuitively in a graphical way. The distribution topology as well as local object structures are represented graphically. Distributed actions such as local actions, network activities, communication and synchronization can be described homogeneously using the same method: graph...

This paper studies a fuzzy graph rewriting with single pushout approach from a viewpoint of fuzzy relational calculus. Two possible kinds of matchings for fuzzy graph rewritings are given, namely, a rigorous matching which just generalizes matchings for crisp (or ordinary) graph rewritings, and an "-matching which represents rather ambiguous or fuzzy one. Finally the pullback structure of fuzzy...