488 research outputs found

    Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)

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    We consider the problem of verifying liveness for systems with a finite, but unbounded, number of processes, commonly known as parameterised systems. Typical examples of such systems include distributed protocols (e.g. for the dining philosopher problem). Unlike the case of verifying safety, proving liveness is still considered extremely challenging, especially in the presence of randomness in the system. In this paper we consider liveness under arbitrary (including unfair) schedulers, which is often considered a desirable property in the literature of self-stabilising systems. We introduce an automatic method of proving liveness for randomised parameterised systems under arbitrary schedulers. Viewing liveness as a two-player reachability game (between Scheduler and Process), our method is a CEGAR approach that synthesises a progress relation for Process that can be symbolically represented as a finite-state automaton. The method is incremental and exploits both Angluin-style L*-learning and SAT-solvers. Our experiments show that our algorithm is able to prove liveness automatically for well-known randomised distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon Protocol). To the best of our knowledge, this is the first fully-automatic method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape

    A randomized encoding of the pi-calculus with mixed choice

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    International audienceWe consider the problem of encoding the pi-calculus with mixed choice into the asynchronous pi-calculus via a uniform translation while preserving a reasonable semantics. Although it has been shown that this is not possible with an exact encoding, we suggest a randomized approach using a probabilistic extension of the asynchronous pi-calculus, and we show that our solution is correct with probability 1 under any proper adversary wrt a notion of testing semantics. This result establishes the basis for a distributed and symmetric implementation of mixed choice which, differently from previous proposals in literature, does not rely on assumptions on the relative speed of processes and it is robust to attacks of proper adversaries

    Self-stabilizing protocol for anonymous oriented bi-directional rings under unfair distributed schedulers with a leader

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    We propose a self-stabilizing protocol for anonymous oriented bi-directional rings of any size under unfair distributed schedulers with a leader. The protocol is a randomized self-stabilizing, meaning that starting from an arbitrary configuration it converges (with probability 1) in finite time to a legitimate configuration (i.e. global system state) without the need for explicit exception handler of backward recovery. A fault may throw the system into an illegitimate configuration, but the system will autonomously resume a legitimate configuration, by regarding the current illegitimate configuration as an initial configuration, if the fault is transient. A self-stabilizing system thus tolerates any kind and any finite number of transient faults. The protocol can be used to implement an unfair distributed mutual exclusion in any ring topology network; Keywords: self-stabilizing protocol, anonymous oriented bi-directional ring, unfair distributed schedulers. Ring topology network, non-uniform and anonymous network, self-stabilization, fault tolerance, legitimate configuration

    Quantitative program logic and expected time bounds in probabilistic distributed algorithms

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    AbstractIn this paper we show how quantitative program logic (Morgan et al., ACM Trans. Programming Languages Systems 18 (1996) 325) provides a formal framework in which to promote standard techniques of program analysis to a context where probability and nondeterminism interact, a situation common to probabilistic distributed algorithms. We show that overall expected time can be formulated directly in the logic and that it can be derived from local properties of components. We illustrate the methods with an analysis of expected running time of the probabilistic dining philosophers (Lehmann and Ravin, Proc 8th Annu. ACM. Symp. on principles of Programming Languages, ACM, New York, 1981, p. 133)

    Value Iteration for Long-run Average Reward in Markov Decision Processes

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    Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks

    Certified Universal Gathering in R2R^2 for Oblivious Mobile Robots

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    We present a unified formal framework for expressing mobile robots models, protocols, and proofs, and devise a protocol design/proof methodology dedicated to mobile robots that takes advantage of this formal framework. As a case study, we present the first formally certified protocol for oblivious mobile robots evolving in a two-dimensional Euclidean space. In more details, we provide a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common orientation nor chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. This result demonstrates both the effectiveness of the approach to obtain new algorithms that use as few assumptions as necessary, and its manageability since the amount of developed code remains human readable.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0160

    Symmetry and similarity in distributed systems

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