We propose an algorithm for parallel state space construction based on an original concurrent data structure, called a localization table, that aims at better spatial and temporal balance. Our proposal is close in spirit to algorithms based on distributed hash tables, with the distinction that states are dynamically assigned to processors; i.e. we do not rely on an a-priori static partition of the state space.In our solution, every process keeps a share of the global state space. Data distribution and coordination between processes is made through the localization table, that is a lockless, thread-safe data structure that approximates the set of states being processed. The localization table is used to dynamically assign newly discovered states and can be queried to return the identity of the processor that own a given state. With this approach, we are able to consolidate a network of local hash tables into an (abstract) distributed one without sacrificing memory affinity -data that are "logically connected" and physically close to each others -and without incurring performance costs associated to the use of locks to ensure data consistency.We evaluate the performance of our algorithm on different benchmarks and compare these results with other solutions proposed in the literature and with existing verification tools.

Verification via model-checking is a very demanding activity in terms of computational resources. While there are still gains to be expected from algorithmic improvements, it is necessary to take advantage of the advances in computer hardware to tackle bigger models. Recent improvements in this area take the form of multiprocessor and multicore architectures with access to large memory space. We address the problem of generating the state space of finitestate transition systems; often a preliminary step for modelchecking. We propose a novel algorithm for enumerative state space construction targeted at shared memory systems. Our approach relies on the use of two data structures: a shared Bloom filter to coordinate the state space exploration distributed among several processors and local dictionaries to store the states. The goal is to limit synchronization overheads and to increase the locality of memory access without having to make constant use of locks to ensure data integrity. Bloom filters have already been applied for the probabilistic verification of systems; they are compact data structures used to encode sets, but in a way that false positives are possible, while false negatives are not. We circumvent this limitation and propose an original multiphase algorithm to perform exhaustive, deterministic, state space generations. We assess the performance of our algorithm on different benchmarks and compare our results with the solution proposed by Inggs and Barringer.

We propose a parallel algorithm for local, on the fly, model checking of a fragment of CTL that is well-suited for modern, multi-core architectures. This model-checking algorithm takes benefit from a parallel state space construction algorithm, which we described in a previous work, and shares the same basic set of principles: there are no assumptions on the models that can be analyzed; no restrictions on the way states are distributed; and no restrictions on the way work is shared among processors. We evaluate the performance of different versions of our algorithm and compare our results with those obtained using other parallel model checking tools. One of the most novel contributions of this work is to study a space-efficient variant for CTL model-checking that does not require to store the whole transition graph but that operates, instead, on a reverse spanning tree.