Circuit Complexity and Multiplicative Complexity of Boolean Functions
نویسندگان
چکیده
In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3− c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key idea of the proof is a circuit complexity measure assigning different weights to XOR and AND gates.
منابع مشابه
The number of boolean functions with multiplicative complexity 2
Multiplicative complexity is a complexity measure defined as the minimum number of AND gates required to implement a given primitive by a circuit over the basis (AND, XOR, NOT). Implementations of ciphers with a small number of AND gates are preferred in protocols for fully homomorphic encryption, multi-party computation and zero-knowledge proofs. In 2002, Fischer and Peralta [12] showed that t...
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