The Exact Multiplicative Complexity of the Hamming Weight Function
نویسندگان
چکیده
We consider the problem of computing the Hamming weight of an n-bit vector using a circuit with gates for addition and multiplication modulo 2 (alternatively, XOR and conjunction gates) only. The number of multiplications necessary and sufficient to build such a circuit is called the “multiplicative complexity” of the Hamming weight function, and is denoted by c∧(H). We prove c∧(H) = n−HN(n) where HN(n) is the Hamming weight of the binary representation of n.
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ورودعنوان ژورنال:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره شماره
صفحات -
تاریخ انتشار 2005