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

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

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

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

Distributed Verification of Rare Properties using Importance Splitting Observers

Rare properties remain a challenge for statistical model checking (SMC) due to the quadratic scaling of variance with rarity. We address this with a variance reduction framework based on lightweight importance splitting observers. These expose the model-property automaton to allow the construction of score functions for high performance algorithms. The confidence intervals defined for importance splitting make it appealing for SMC, but optimising its performance in the standard way makes distribution inefficient. We show how it is possible to achieve equivalently good results in less time by distributing simpler algorithms. We first explore the challenges posed by importance splitting and present an algorithm optimised for distribution. We then define a specific bounded time logic that is compiled into memory-efficient observers to monitor executions. Finally, we demonstrate our framework on a number of challenging case studies

A Parallel Divide-and-Conquer based Evolutionary Algorithm for Large-scale Optimization

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to solve the emerging large-scale problems both effectively and efficiently. In this paper, we propose a novel Divide-and-Conquer (DC) based EA that can not only produce high-quality solution by solving sub-problems separately, but also highly utilizes the power of parallel computing by solving the sub-problems simultaneously. Existing DC-based EAs that were deemed to enjoy the same advantages of the proposed algorithm, are shown to be practically incompatible with the parallel computing scheme, unless some trade-offs are made by compromising the solution quality.Comment: 12 pages, 0 figure

Symmetry reduction and heuristic search for error detection in model checking

The state explosion problem is the main limitation of model checking. Symmetries in the system being verified can be exploited in order to avoid this problem by defining an equivalence (symmetry) relation on the states of the system, which induces a semantically equivalent quotient system of smaller size. On the other hand, heuristic search algorithms can be applied to improve the bug finding capabilities of model checking. Such algorithms use heuristic functions to guide the exploration. Bestfirst is used for accelerating the search, while A* guarantees optimal error trails if combined with admissible estimates. We analyze some aspects of combining both approaches, concentrating on the problem of finding the optimal path to the equivalence class of a given error state. Experimental results evaluate our approach

Quantitative program logic and expected time bounds in probabilistic distributed algorithms

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)