Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this paper, we use the coalgebraic view on systems to derive, in a uniform way, abstract procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization. First, we show that for coalgebras in categories equipped with factorization structures, there exists an abstract procedure for equivalence checking. Then, we consider coalgebras in categories without suitable factorization structures: under certain conditions, it is possible to apply the above procedure after transforming coalgebras with reflections. This transformation can be thought of as some kind of determinization. We will apply our theory to the following examples: conditional transition systems and (non-deterministic) automata.

Abstract. We consider conditional reactive systems, a general abstract framework for rewriting, in which reactive systemsà la Leifer and Milner are enriched with (nested) application conditions. We study the problem of deriving labelled transitions and bisimulation congruences from a reduction semantics. That is, we synthesize interactions with the environment in order to obtain a compositional semantics. Compared to earlier work we not only address the problem of deriving information about the (minimal) context needed to obtain a full left-hand side and thus be able to perform a reduction, but also generate conditions on the remaining context.

Model transformation is a prime technique in modern, model-driven software design. One of the most challenging issues is to show that the semantics of the models is not affected by the transformation. So far, there is hardly any research into this issue, in particular in those cases where the source and target languages are different.In this paper, we are using two different state-of-the-art proof techniques (explicit bisimulation construction versus borrowed contexts) to show bisimilarity preservation of a given model transformation between two simple (self-defined) languages, both of which are equipped with a graph transformation-based operational semantics. The contrast between these proof techniques is interesting because they are based on different model transformation strategies: triple graph grammars versus in situ transformation. We proceed to compare the proofs and discuss scalability to a more realistic setting.Partially supported by DFG project Behaviour-GT.

No abstract

No abstract