Abstract:We show that the set of all functions is equivalent to the set of all symmetric functions up to deterministic time complexity. In particular, for any function f , there is an equivalent symmetric function f sym such that f can be computed form f sym and vice-versa (modulo an extra deterministic linear time computation). For f over finite fields, f sym is (necessarily) over an extension field. This reduction is optimal in size of the extension field. For polynomial functions, the degree of f sym is not optimal.… Show more
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