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.

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 is a technique that can help alleviate the problem of state space explosion in model checking. The idea is to verify only a subset of states from each class (orbit) of symmetric states. This paper presents a framework for symmetry reduced model checking of B machines, which verifies a unique representative from each orbit. Symmetries are induced by the deferred set; a key component of the B language. This contrasts with strategies that require the introduction of a special data type into a language, to indicate symmetry. An extended version of the graph isomorphism program, textitnauty, is used to detect symmetries, and the symmetry reduction package has been integrated into the ProB model checker. Experimental results illustrate the effectiveness of the method, where exponential speedups are sometimes possible. Relevant algorithms are presented, and there is a comparison with an alternate symmetry reduction strategy, called permutation flooding.