Maciej Gazda

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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)
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)
Labelled transition systems constitute a widely used model of concurrent computation. They model processes by explicitly describing their states and transitions from state to state, together with the actions that produce these transitions. Several notions of behavioural semantics have been proposed, with the aim to identify those states that afford the same(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)
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/⌊d/2⌋)⌊d/2⌋) time. Computing a winning strategy for the other player requires a re-run of the algorithm(More)