88 research outputs found
A linear translation from LTL to the first-order modal µ-calculus
The modal µ-calculus is a very expressive temporal logic. In particular, logics such as LTL, CTL and CTL* can be translated into the modal mu-calculus, although existing translations of LTL and CTL* are at least exponential in size. We show that an existing simple first-order extension of the modal µ-calculus allows for a linear translation from LTL. Furthermore, we show that solving the translated formulae is as efficient as the best known methods to solve LTL formulae directly
Parity game reductions
Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the size of the games, which, for model checking problems, can easily contain vertices or beyond. Equivalence relations can be used to reduce the size of a parity game, thereby potentially alleviating part of the computational burden. We reconsider (governed) bisimulation and (governed) stuttering bisimulation, and we give detailed proofs that these relations are equivalences, have unique quotients and they approximate the winning regions of parity games. Furthermore, we present game-based characterisations of these relations. Using these characterisations our equivalences are compared to relations for parity games that can be found in the literature, such as direct simulation equivalence and delayed simulation equivalence. To complete the overview we develop coinductive characterisations of direct- and delayed simulation equivalence and we establish a lattice of equivalences for parity games
Parity game reductions
Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the size of the games, which, for model checking problems, can easily contain vertices or beyond. Equivalence relations can be used to reduce the size of a parity game, thereby potentially alleviating part of the computational burden. We reconsider (governed) bisimulation and (governed) stuttering bisimulation, and we give detailed proofs that these relations are equivalences, have unique quotients and they approximate the winning regions of parity games. Furthermore, we present game-based characterisations of these relations. Using these characterisations our equivalences are compared to relations for parity games that can be found in the literature, such as direct simulation equivalence and delayed simulation equivalence. To complete the overview we develop coinductive characterisations of direct- and delayed simulation equivalence and we establish a lattice of equivalences for parity games
Abstraction in parameterised Boolean equation systems
We present a general theory of abstraction for a variety of verification problems. Our theory is set in the framework of parameterized Boolean equation systems. The power of our abstraction theory is compared to that of generalised Kripke modal transition systems (GTSs). We show that for model checking the modal µ-calculus, our abstractions can be exponentially more succinct than GTSs and our theory is as complete as the GTS framework for abstraction. Furthermore, we investigate the completeness of our theory for verification problems other than the modal µ-calculus. We illustrate the potential of our theory through case studies using the first-order modal µ-calculus and a real-time extension thereof, conducted using a prototype implementation of a new syntactic transformation for equation systems
Model Checking the FlexRay Startup Phase
This report describes a discrete-time model of the startup phase of a FlexRay network. The startup behaviour of this network is analysed in the presence of several faults. It is shown that in certain cases a faulty node can prevent the network from communicating altogether. One previously unknown scenario is uncovered
Oink: an Implementation and Evaluation of Modern Parity Game Solvers
Parity games have important practical applications in formal verification and
synthesis, especially to solve the model-checking problem of the modal
mu-calculus. They are also interesting from the theory perspective, as they are
widely believed to admit a polynomial solution, but so far no such algorithm is
known. In recent years, a number of new algorithms and improvements to existing
algorithms have been proposed. We implement a new and easy to extend tool Oink,
which is a high-performance implementation of modern parity game algorithms. We
further present a comprehensive empirical evaluation of modern parity game
algorithms and solvers, both on real world benchmarks and randomly generated
games. Our experiments show that our new tool Oink outperforms the current
state-of-the-art.Comment: Accepted at TACAS 201
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