4 research outputs found
Conditional Bigraphs
Bigraphs are a universal graph based model, designed for analysing reactive systems that include spatial and non-spatial (e.g. communication) relationships. Bigraphs evolve over time using a rewriting framework that finds instances of a (sub)-bigraph, and substitutes a new bigraph. In standard bigraphs, the applicability of a rewrite rule is determined completely by a local match and does not allow any non-local reasoning, i.e. contextual conditions. We introduce conditional bigraphs that add conditions to rules and show how these fit into the matching framework for standard bigraphs. An implementation is provided, along with a set of examples. Finally, we discuss the limits of application conditions within the existing matching framework and present ways to extend the range of conditions that may be expressed
Rewriting Abstract Structures: Materialization Explained Categorically
The paper develops an abstract (over-approximating) semantics for
double-pushout rewriting of graphs and graph-like objects. The focus is on the
so-called materialization of left-hand sides from abstract graphs, a central
concept in previous work. The first contribution is an accessible, general
explanation of how materializations arise from universal properties and
categorical constructions, in particular partial map classifiers, in a topos.
Second, we introduce an extension by enriching objects with annotations and
give a precise characterization of strongest post-conditions, which are
effectively computable under certain assumptions