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- Symmetric Boolean Functions; NP-Completeness; Conjugate Symmetry; Generalized Symmetry
The problem of detecting virtually any type of symmetry is shown to be co-NP-complete. We start with totally symmetric functions, then extend the result to partially symmetric functions, then to more general cofactor relations, and finally to generic permutation-group symmetries. We also show that the number of types of symmetry grows substantially with the number of inputs, compounding the complexity of an already difficult problem.