Mathias Hülsbusch

A coalgebraic perspective on minimization and determinization

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.

Showing full semantics preservation in model transformation: a comparison of techniques

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.

Specification and Verification of Model Transformations

Model transformations are a key concept within model driven development and there is an enormous need for suitable formal analysis techniques for model transformations, in particular with respect to behavioural equivalence of source models and their corresponding target models. For this reason, we discuss the general challenges that arise for the specification and verification of model transformations and present suitable formal techniques that are based on graph transformation. In this context, triple graph grammars show many benefits for the specification process, e.g. modelers can work on an intuitive level of abstraction and there are formal results for syntactical correctness, completeness and efficient execution. In order to verify model transformations with respect to behavioural equivalence we apply well-studied techniques based on the double pushout approach with borrowed context, for which the model transformations specified by triple graph transformation rules are flattened to plain (in-situ) graph transformation rules. The potential and adequateness of the presented techniques are demonstrated by an intuitive example, for which we show the correctness of the model transformation with respect to bisimilarity of source and target models.

Conditional Reactive Systems

We lift the notion of nested application conditions from graph transformation systems to the general categorical setting of reactive systems as defined by Leifer and Milner. This serves two purposes: first, we enrich the formalism of reactive systems by adding application conditions for rules; second, it turns out that some constructions for graph transformation systems (such as computing weakest preconditions and strongest postconditions and showing local confluence by means of critical pair analysis) can be done very elegantly in the more general setting.

Deriving bisimulation congruences for conditional reactive systems

We consider conditional reactive systems, a general abstract framework for rewriting, in which reactive systems a 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.

Towards Alternating Automata for Graph Languages

In this paper we introduce alternating automata for languages of arrows of an arbitrary category, and as an instantiation thereof alternating automata for graph languages. We study some of their closure properties and compare them, with respect to expressiveness, to other methods for describing graph languages. We show, by providing several examples, that many graph properties (of graphs of bounded path width) can be naturally expressed as alternating automata.