Graph transformation is a rapidly expanding field of research, motivated by a wide range of applications. Such transformations can be specified at different levels of abstraction. On one end, there are “programmed” graph transformation systems with very fine control over manipulation of individual graph items. Different flavours of rule-based graph transformation systems match their patterns in...

In this paper we define recursive rules in the double pushout approach (DPO) to graph transformation. Classical DPO rules are extended with a base case condition and a recursion condition. Mechanisms are provided to pass the match from both conditions to the rule’s left hand side, and also between two consecutive steps in the recursion. The approach is useful when recursive structures (such as ...

Motivated by recent work on the derivation of labelled transitions and bisimulation congruences from unlabelled reaction rules, we show how to solve this problem in the DPO (double-pushout) approach to graph rewriting. Unlike in previous approaches, we consider graphs as objects, instead of arrows, of the category under consideration. This allows us to present a very simple way of deriving labe...

We proceed with the study of termination properties in the double pushout approach to algebraic rewriting, and show a concrete termination criterion for rewriting systems with inhibitors. Inhibitors prevent elements in an algebra to participate in rule matches, so that termination depends only on whether new possibilities for matches are created. The notion of inhibitor can be extended to consi...

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 ...

Reconfigurable place/transition systems are Petri nets with initial markings and a set of rules which allow the modification of the net during runtime in order to adapt the net to new requirements. For the transformation of Petri nets in the double pushout approach, the categorical framework of adhesive high-level replacement systems has been instantiated to Petri nets. In this paper, we show t...

Using twisted and formal-local methods, we prove that every separated algebraic space which is the (open/flat) pushout of affine schemes has enough Azumaya algebras. As a corollary show that, under mild hypothesis, cohomological Brauer class representable by an algebra away from closed subset codimension $\geq 3$, generalizing early result Grothendieck. Next, $\mathrm{Br}(X)=\mathrm{Br}'(X)$ wh...

This thesis is concerned with the development of a theory which, given a formalism with a reduction semantics, allows the derivation of a canonical labelled transition system on which bisimilarity as well as other other equivalences are congruences; provided that the contexts of the formalism form a category which has certain colimits. We shall begin by extending Leifer and Milner’s theory of r...

Abstract Over the last 20 years, finite element analysis (FEA) has become a standard tool for metal joining processes. When FEA tools are combined with design of experiments (DOE) methodologies, academic research shown potential virtual DOE to allow rapid manufacturing parameters and their influence on final formed products. However, within domain bulk-metal joining, rarely used in industrial a...

Abstract In this paper, we address the problem of proving confluence for string diagram rewriting, which was previously shown to be characterised combinatorially as double-pushout rewriting with interfaces (DPOI) on (labelled) hypergraphs. For standard DPO without interfaces, terminating systems is, in general, undecidable. Nevertheless, show here that DPOI, and hence is decidable. We apply res...