By proving the correspondence between the usual double-pushout approach and Banach’s inward version in a purely categorical setting, we can extend the latter to noninjective left-hand sides. In the injective case, Banach’s point of view establishes a close relationship between the categorical approach and Kaplan’s ∆-grammars allowing a slight generalization of ∆-grammars and making them an oper...

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.

We introduce Single-Pushout Rewriting for arbitrary partial algebras. Thus, we give up the usual restriction to graph structures, which are algebraic categories with unary operators only. By this generalisation, we obtain an integrated and straightforward treatment of graphical structures (objects) and attributes (data). We lose co-completeness of the underlying category. Therefore, a rule is n...

We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting with strong matching. Our approach, called PBPO $$^{+}$$ , exerts more control over embedding of pattern in host graph, which is important a large class rewrite systems. In addition, we show that well-suited labeled graphs and certain classes attributed graphs. For this purpose, employ lattice structure on label set use...

We analyse extensions $\Sigma$ of groupoids G by bundles A abelian groups. describe a pushout construction for such extensions, and use it to the extension group given groupoid bundle A. There is natural action Sigma on dual A, yielding corresponding transformation groupoid. The this map from fibre product with its Cartesian circle twist over resulting prove that full C*-algebra isomorphic $\Si...

We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is new formulation of double pushout on which explicitly records boundary rewrite. Using this structure augment these with rotation system, allowing surface topolog...

We give a hypergraph rewriting semantics for the polyadic π-calculus, based on rewriting rules equivalent to those in the double-pushout approach. The structural congruence of the π-calculus is replaced by hypergraph isomorphism. The correctness of the encoding from the graph-based notation into π-calculus can be shown by using an intermediate notation, so-called name-based graph terms.

In this paper, we introduce contextual hypergraph grammars, which generalize the total contextual string grammars. We study the position of the class of languages generated by contextual hypergraph grammars in comparison with graph languages generated by hyperedge replacement grammars and double-pushout hypergraph grammars. Moreover, several examples show the potential of the new class of gramm...

Abstract Graphical notations are already popular for the design of software, as witnessed by the success of the Uniform Modeling Languages (UML). In this paper, we advocate the use of graphs and graph transformation for programming graph-based systems. Our case study, the flattening of hierarchical statecharts, reveals that cloning, a recently proposed transformation concept, makes graph transf...