We present a definition of term graph rewriting as the taking of a pushout in a category of partial morphisms, adapting the rather ad hoc definitions we gave in [Ken87] so as to use a standard category-theoretic concept of partial morphism. This single-pushout construction is shown to coincide with the well-known double-pushout description of graph rewriting whenever the latter is defined. In g...

The single-pushout approach to graph transformation interprets a double-pushout transformation rule of the classical algebraic approach which consists of two rotul graph morphisms as a single particll morphism from the left-to the right-hand side. The notion of a double-pushout diagram for the transformation process can then be substituted by a single-pushout diagram in an appropriate category ...

Debashis Basak Fore Systems Warrendale, PA, USA Abhijit K. Choudhury Bell Laboratories Holmdel, NJ, USA Ellen L. Hahne Bell Laboratories Holmdel, NJ, USA Abstract We study a multistage ATM switch in which shared-memory switching elements are arranged in a banyan topology. By \shared-memory", we mean that each switching element uses output queueing and shares its local cell bu er memory among al...

The problem of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets has been faced several times along the years, both for the single-pushout and double-pushout approaches, but only partial results were obtained. In this paper we fully extend Winskel’s approach to single-pushout grammars providing them with a categorical concurrent semantics ...

Studying parallelism and concurrency in the double-pushout approach to graph transformations is mainly based on the so-called triple-pushout condition. The categories of sets and of graphs satisfy this condition. If we, however, consider graph morphisms that may change the labels in a welldefined manner (structurally labeled graphs), the triple-pushout condition does no longer hold true. In thi...

In category theory, most set-theoretic constructions—union, intersection, etc.—have direct categorical counterparts. But up to now, there is no direct construction of a deletion operation like the set-theoretic complement. In rule-based transformation systems, deletion of parts of a given object is one of the main tasks. In the double pushout approach to algebraic graph transformation, the cons...

We tackle the problem of graph transformation with a particular focus on node cloning. We propose a graph rewriting framework where nodes can be cloned zero, one or more times. A node can be cloned together with all its incident edges, with only the outgoing edges, with only the incoming edges or without any of the incident edges. We thus subsume previous works such as the sesqui-pushout, the h...

In this paper we study single-pushout transformation in a category of spans, a generalization of the notion of partial morphism in, for instance, 2,4]. As an application, single-pushout transformation in a category of hypergraphs with a special type of partial morphisms, the conformisms, is presented. In particular , we show the existence of the pushout of any pair of conformisms of hypergraphs...

Sesqui-pushout (sqpo) rewriting—“sesqui” means “one and a half” in Latin—is a new algebraic approach to abstract rewriting in any category. sqpo rewriting is a deterministic and conservative extension of double-pushout (dpo) rewriting, which allows to model “deletion in unknown context”, a typical feature of single-pushout (spo) rewriting, as well as cloning. After illustrating the expressivene...