We consider the bit-complexity (i.e.a, total number of bits transmitted) of computing boolean functions on an anonymous canonically labeled n-dimensional hypercube network and give a characterization of the boolean functions computable on such a network as exactly those boolean functions which are invariant under all bit-complement automorphisms of the hyercube. We provide an efficient algorithm for computing all such functions with bit complexity O(N · log4 N). For the case of symmetric boolean functions we give an algorithm with bit complexity O(N · log2 N).

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Journal Journal of Algorithms
Kranakis, E, & Krizanc, D. (Danny). (1997). Distributed Computing on Anonymous Hypercube Networks. Journal of Algorithms, 23(1), 32–50.