Documenting and designing QVTo model transformations through mathematics

Model transformations play an essential role in Model Driven Engineering (MDE), as they provide the means to use models as first-class artifacts in the software development process. While there exist a number of languages specifically designed to program model transformations, the practical challenges of documenting and designing model transformations are hardly addressed. In this paper we demonstrate how QVTo model transformations can be described and designed informally through the mathematical notation of set theory and functions. We align the QVTo concepts with the mathematical concepts, and, building on the latter, we formulate two design principles of developing QVTo transformations: structural decomposition and chaining model transformations

Strategy derivation for small progress measures

Small Progress Measures is one of the most efficient parity game solving algorithms. The original algorithm provides the full solution (winning regions and strategies) in $O(dm \cdot (n/ \lceil d/2 \rceil)^{\lceil d/2 \rceil} )$ time, and requires a re-run of the algorithm on one of the winning regions. We provide a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning strategies for both players in one pass. This reduces the upper bound on strategy derivation for SPM to $O(dm \cdot (n/ \lceil d/2 \rceil)^{\lceil d/2 \rceil} )$

Improvement in small progress measures

Small Progress Measures is one of the classical parity game solving algorithms. For games with n vertices, m edges and d different priorities, the original algorithm computes the winning regions and a winning strategy for one of the players in O(dm.(n/floor(d/2))^floor(d/2)) time. Computing a winning strategy for the other player requires a re-run of the algorithm on that player's winning region, thus increasing the runtime complexity to O(dm.(n/ceil(d/2))^ceil(d/2)) for computing the winning regions and winning strategies for both players. We modify the algorithm so that it derives the winning strategy for both players in one pass. This reduces the upper bound on strategy derivation for SPM to O(dm.(n/floor(d/2))^floor(d/2)). At the basis of our modification is a novel operational interpretation of the least progress measure that we provide

Folk theorems on the correspondence between state-based and event-based systems

Kripke Structures and Labelled Transition Systems are the two most prominent semantic models used in concurrency theory. Both models are commonly believed to be equi-expressive. One can find many ad-hoc embeddings of one of these models into the other. We build upon the seminal work of De Nicola and Vaandrager that firmly established the correspondence between stuttering equivalence in Kripke Structures and divergence-sensitive branching bisimulation in Labelled Transition Systems. We show that their embeddings can also be used for a range of other equivalences of interest, such as strong bisimilarity, simulation equivalence, and trace equivalence. Furthermore, we extend the results by De Nicola and Vaandrager by showing that there are additional translations that allow one to use minimisation techniques in one semantic domain to obtain minimal representatives in the other semantic domain for these equivalences

Cooking your own parity game preorders through matching plays

\u3cp\u3eParity games can be used to solve satisfiability, verification and controller synthesis problems. As part of an effort to better understand their nature, or the nature of the problems they solve, preorders on parity games have been studied. Defining these relations, and in particular proving their transitivity, has proven quite difficult on occasion. We propose a uniform way of lifting certain preorders on Kripke structures to parity games and study the resulting preorders. We explore their relation with parity game preorders from the literature and we study new relations. Finally, we investigate whether these preorders can also be obtained via modal characterisations.\u3c/p\u3