One of the basic sanity properties of a behavioural semantics is that it constitutes a congruence with respect to standard process operators. This issue has been traditionally addressed by the development of rule formats for transition system specifications that define process algebras. In this paper we suggest a novel, orthogonal approach. Namely, we focus… (More)
Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free µ-calculus and ECTL * model checking problems. These classes can be solved in polynomial time using dedicated algorithms. We investigate the complexity of Zielonka's Recursive algorithm for solving these special games, showing that the… (More)
We prove a compactness theorem in the context of Hennessy-Milner logic. It is used to derive a sufficient condition on modal characterizations for the Approximation Induction Principle to be sound modulo the corresponding process equivalence. We show that this condition is necessary when the equivalence in question is compositional with respect to the… (More)
Inspired by the concept of a consistent correlation for Boolean equation systems, we introduce and study a novel relation, called consistent consequence. We show that it can be used as an approximation of the solution to an equation system. For the closed, simple and recursive fragment of equation systems we prove that it coincides with direct simulation… (More)
We study two notions of expressiveness, which have appeared in abstraction theory for model checking , and find them incomparable in general. In particular, we show that according to the most widely used notion, the class of Kripke Modal Transition Systems is strictly less expressive than the class of Generalised Kripke Modal Transition Systems (a… (More)
An existing axiomatisation strategy for process algebras modulo bisimulation semantics can be extended so that it can be applied to other behavioural semantics as well. We study term rewriting properties of the resulting axiomatisations.
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 · (n/⌈d/2⌉) ⌈d/2⌉) time, and requires a rerun of the algorithm on one of the winning regions. We provide a novel operational interpretation of progress measures, and modify the… (More)
We present a theory of abstraction for the framework of parameterised Boolean equation systems, a first-order fixpoint logic. Parameterised Boolean equation systems can be used to solve a variety of problems in verification. We study the capabilities of the abstraction theory by comparing it to an abstraction theory for Generalised Kripke modal Transition… (More)