Conditional Bisimilarity for Reactive Systems

Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to obtain a compositional semantics. We enrich the notion of reactive systems by conditions on two levels: first, as in earlier work, we consider rules enriched with application conditions and second, we investigate the notion of conditional bisimilarity. Conditional bisimilarity allows us to say that two system states are bisimilar provided that the environment satisfies a given condition. We present several equivalent definitions of conditional bisimilarity, including one that is useful for concrete proofs and that employs an up-to-context technique, and we compare with related behavioural equivalences. We consider examples based on DPO graph rewriting, an instantiation of reactive systems.

Graph rewriting rules for RDF database evolution: optimizing side-effect processing

Purpose Graph rewriting concerns the technique of transforming a graph; it is thus natural to conceive its application in the evolution of graph databases. This paper aims to propose a two-step framework where rewriting rules formalize instance or schema changes, ensuring graph’s consistency with respect to constraints, and updates are managed by ensuring rule applicability through the generation of side effects: new updates which guarantee that rule application conditions hold. Design/methodology/approach This paper proposes Schema Evolution Through UPdates, optimized version (SetUpOPT), a theoretical and applied framework for the management of resource description framework (RDF)/S database evolution on the basis of graph rewriting rules. The framework is an improvement of SetUp which avoids the computation of superfluous side effects and proposes, via SetUpoptND, a flexible and extensible package of solutions to deal with non-determinism. Findings This paper shows graph rewriting into a practical and useful application which ensures consistent evolution of RDF databases. It introduces an optimised approach for dealing with side effects and a flexible and customizable way of dealing with non-determinism. Experimental evaluation of SetUpoptND demonstrates the importance of the proposed optimisations as they significantly reduce side-effect generation and limit data degradation. Originality/value SetUp originality lies in the use of graph rewriting techniques under the closed world assumption to set an updating system which preserves database consistency. Efficiency is ensured by avoiding the generation of superfluous side effects. Flexibility is guaranteed by offering different solutions for non-determinism and allowing the integration of customized choice functions.