Abstract. Symmetry reduction is an established method for limiting the amount of states that have to be checked during exhaustive model checking. The idea is to only verify a single representative of every class of symmetric states. However, computing this representative can be nontrivial, especially for a language such as B with its involved data structures and operations. In this paper, we propose an alternate approach, called permutation flooding. It works by computing permutations of newly encountered states, and adding them to the state space. This turns out to be relatively unproblematic for B's data structures and we have implemented the algorithm inside the ProB model checker. Empirical results confirm that this approach is effective in practice; speedups exceed an order of magnitude in some cases. The paper also contains correctness results of permutation flooding, which should also be applicable for classical symmetry reduction in B.
Symmetry reduction holds great promise to counter the state explosion problem. However, currently it is "conducting a life on the fringe", and is not widely applied, mainly due to the restricted applicability of many of the techniques. In this paper we propose a symmetry reduction technique applied to high-level formal specification languages (B and Z). Not only does symmetry arise naturally in most models, it can also be exploited without restriction by our method. This method translates states of a formal model into directed graphs, and then uses graph canonicalisation to detect symmetries. We use the tool NAUTY to efficiently perform graph canonicalisation, which we have interfaced with the model checker PROB.In this paper we present the general technique, show how states can be translated first into vertex-coloured graphs suitable for NAUTY. We present empirical results, showing the effectiveness of our method as well as analysing the cost of graph canonicalisation.
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