It is often the case that systems are "nearly symmetric"; they exhibity symmetry in a part of their description but are, nevertheless, globally asymmetric. We formalize several notions of near symmetry and show how to obtain the nenefits of symmetry reduction when applied to asymmetric systems which are nearly symmetric. We show that for some nearly symmetric systems it is possible to perform symmetry reduction and obtain a bisimilar (up to permutation) symmetry reduced system. Using a more general notion of "sub-symmetry" we show how to generate a reduced structure that is simulated (up to permutation) by the original asymmetric program.
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