Parallel Partial Order Reduction with Topological Sort Proviso

Abstract

Partial order reduction and distributed-memory processing are the two essential techniques to fight the well-known state space explosion problem in explicit state model checking. Unfortunately, these two techniques have not been integrated yet to a satisfactory degree. While for verification of safety properties, there are a few rather successful approaches to parallel partial order reduction, for LTL model checking all suggested approaches are either too technically involved to be smoothly incorporated with the existing parallel algorithms, or they are simply weak in the sense that the achieved reduction in the size of the state space is minor. The main source of difficulties is the cycle proviso that requires one fully expanded state on every cycle in the reduced state space graph. This can be easily achieved in the sequential case by employing depth-first search strategy for state space generation. Unfortunately, this strategy is incompatible with parallel (hence distributed-memory) processing, which limits application of partial order reduction technique to the sequential case. In this paper we suggest a new technique that guarantees correct construction of the reduced state space graph w.r.t. the cycle proviso. Our new technique is fully compatible with the parallel graph traversal procedure while at the same time it provides competitive reduction of the state space if compared to the serial case. The new technique has been implemented within the parallel and distributed-memory LTL model checker DiVinE and its performance is reported in this paper.