### Vector Symmetry Reduction

#### Abstract

Symmetry reduction is an effective state-space reduction technique for model checking, and works by restricting search to equivalence class representatives with respect to a group of symmetries for a model. A major problem with symmetry reduction techniques is the time taken to compute the representative of a state, which can be prohibitive. In efficient implementations of symmetry reduction, a symmetry is applied to a state as a sequence of operations which swap component identities. We show that vector processing technology, common to modern computers, can be used to implement a vectorised swap operation, which can be incorporated into the representative computation algorithm to accelerate symmetry reduction. Via a worked example, we present details of this vector symmetry reduction method. We have implemented our techniques in the TopSPIN symmetry reduction package for the SPIN model checker, and present experimental results showing the speedups obtained via vectorisation for two case-studies running on a PowerPC vector processor.