We consider the relationship between three ways of defining graph derivability. That the traditional double-pushout approach and Banach’s inward version are equivalent in the case of injective left-hand side is proved in a purely categorical setting. In the case of noninjective left-hand sides, equivalence can be shown in special categories if the righthand side is injective. Both approaches ha...

We present an approach to attributed graph transformation which requires neither infinite graphs containing data algebras nor auxiliary edges that link graph items with their attributes. Instead, we use the double-pushout approach with relabelling and extend it with rule schemata which are instantiated to ordinary rules prior to application. This framework provides the formal basis for the grap...

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well t...

It is well known that the category of finite sets and cospans, composed by pushout, contains the universal special commutative Frobenius algebra. In this note we observe that the same construction yields also general commutative Frobenius algebras, if just the pushouts are changed to homotopy pushouts.

It is shown that it is undecidable in general whether a graph rewriting system (in the \double pushout approach") is terminating. The proof is by a reduction of the Post Correspondence Problem. It is also argued that there is no straightforward reduction of the halting problem for Turing machines or of the termination problem for string rewriting systems to the present problem.

In recent work with Vincent Danos and Jean Krivine the author introduced a general framework for backtracking in concurrent formalisms, thus allowing modelling of situations where deadlock can arise without the necessity of explicitly encoding the often involved backtracking mechanisms. Here we shall discuss how the framework can be applied to the well-known formalism of double-pushout graph tr...

The new approach of distributed graphs and graph transformation as developed in this article allows to use structured graph transformation on two abstraction levels, the network and the local level. The network level contains the description of the topological structures of a system. The local level covers the description of states and their transitions in local systems. Local state transitions...

The interfacial strength of secondary osteons from the diaphysis of the Thoroughbred equine third metacarpal was evaluated using the fiber pushout test. The pushout was performed on 300-500 microm sections of 4x4x15 mm bone blocks machined from four anatomic regions of the cortex. Pushout strength was evaluated from proximal to distal location within the diaphysis on four osteon types classifie...

Graph grammars have been introduced in the late 1970s [1], then they have been significantly improved up to the 2000s [2]. A lot of significant results are due to H. Ehrig and his colleagues who have conceived an algebraic approach to graph rewriting by the means of category theory [1]. It opened the way to computations with attributes. In this approach, when dealing with model transformations,...

We present a simple, abstract approach that allows to integrate graph attribution into the graph structure itself. We use a declarative setting where the calculation of the attributions relies on single-pushout derivations in a category of total homomorphisms. We discuss applications to term graph typing, including multi-level typing and type classes, and visualisation of compilation.