We presentMLSolver, a tool for solving the satisfiability and validity problems for modal fixpoint logics. The underlying technique is based on characterisations of satisfiability through infinite (cyclic) tableaux in which branches have an inner thread structure mirroring the regeneration of least and greatest fixpoint constructs in the infinite. Well-foundedness for unfoldings of least fixpoints is checked using deterministic parity automata. This reduces the satisfiability and validity problems to the problem of solving a parity game. MLSolver then uses a parity game solver in order to decide satisfiability and derives example models from the winning strategies in the parity game. Currently supported logics are the modal and linear-time

Abstract. We endow action sets of transition systems with a partial order that expresses the degree of specialization of actions, and with an intuitive but flexible consistency predicate that constrains the extension of such orders with more specialized actions. We develop a satisfaction relation for such models and the µ-calculus. We then prove that this satisfaction relation is sound for Thomsen’s extended bisimulation as our refinement notion for models, even for consistent extensions of ordered action sets. We then demonstrate how this satisfaction relation can be reduced, fairly efficiently, to classical µ-calculus model checking. These results provide formal support for change management of models and their validation (e.g. in model-centric software development), and enable verification of concrete systems with respect to properties specified for abstract actions. 1

Focus games have been shown to yield game-theoretical characterisations for the satisfiability and the model checking problem for various temporal logics. One of the players is given a tool -- the focus -- that enables him to show the regeneration of temporal operators characterised as least or greatest fixpoints. His strategy usually is build upon a priority list of formulas and, thus, is not positional. This paper defines foci games for satisfiability of LTL formulas. Strategies in these games are trivially positional since they parallelise all of the focus player's choices, thus resulting in a 1-player game in e#ect. The games are shown to be correct and to yield smaller (counter-)models than the focus games. Finally, foci games for model checking LTL are defined as well.

Abstract—We present a symbolic model checking algorithm for verification of Nash equilibria in finite state mechanisms modeling Multiple Administrative Domains (MAD) distributed systems. Given a finite state mechanism, a proposed protocol for each agent and an indifference threshold for rewards, our model checker returns PASS if the proposed protocol is a Nash equilibrium (up to the given indifference threshold) for the given mechanism, FAIL otherwise. We implemented our model checking algorithm inside the NuSMV model checker and present experimental results showing its effectiveness for moderate size mechanisms. I.

Abstract. Model checking games are instances of Hintikka’s game semantics for logic used for purposes of debugging systems verification models. Previous work in the area has developed these games for branching time logic. The paper develops an extension to a logic that adds epistemic operators, and interprets the branching time operators with respect to fairness constraints. The implementation of the extended games in the epistemic model checker MCK is described. 1

The problem of solving a parity game is at the core of many problems in model checking, satisfiability checking and program synthesis. Some of the best algorithms for solving parity game are strategy improvement algorithms. These are global in nature since they require the entire parity game to be present at the beginning. This is a distinct disadvantage because in many applications one only needs to know which winning region a particular node belongs to, and a witnessing winning strategy may cover only a fractional part of the entire game graph. We present a local strategy improvement algorithm which explores the game graph on-the-fly whilst performing the improvement steps. We also compare it empirically with existing global strategy improvement algorithms and the currently only other local algorithm for solving parity games. It turns out that local strategy improvement can outperform these others by several orders of magnitude. 1