منابع مشابه
Efficient quantum protocols for XOR functions
We show that for any Boolean function f : {0, 1} → {0, 1}, the bounded-error quantum communication complexity Q (f ◦ ⊕) of XOR functions f(x ⊕ y) satisfies that Q (f ◦ ⊕) = O ( 2 ( log ‖f̂‖1, + log n ) log(1/ ) ) , where d = deg2(f) is the F2-degree of f , and ‖f̂‖1, = ming:‖f−g‖∞≤ ‖ĝ‖1. This implies that the previous lower bound Q (f ◦ ⊕) = Ω(log ‖f̂‖1, ) by Lee and Shraibman [LS09] is tight for ...
متن کاملProbabilities of 2-Xor Functions
The problem 2-Xor-Sat asks for the probability that a random expression, built as a conjunction of clauses x ⊕ y, is satisfiable. We consider here a refinement of this question, namely the probability that a random expression computes a specific Boolean function. The answer involves a description of 2-Xor expressions as multigraphs, and uses classical methods of analytic combinatorics.
متن کاملCommunication Complexities of XOR functions
We call F : {0, 1}n×{0, 1}n → {0, 1} a symmetric XOR function if for a function S : {0, 1, ..., n} → {0, 1}, F (x, y) = S(|x⊕ y|), for any x, y ∈ {0, 1}n, where |x⊕ y| is the Hamming weight of the bit-wise XOR of x and y. We show that for any such function, (a) the deterministic communication complexity is always Θ(n) except for four simple functions that have a constant complexity, and (b) up ...
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This paper presents a unified and simple treatment of basic questions concerning two computational models: multiparty communication complexity and polynomials over GF(2). The key is the use of (known) norms on Boolean functions, which capture their proximity to each of these models (and are closely related to property testers of this proximity). The main contributions are new XOR lemmas. We sho...
متن کاملOn the communication complexity of XOR functions
An XOR function is a function of the form g(x, y) = f(x ⊕ y), for some boolean function f on n bits. We study the quantum and classical communication complexity of XOR functions. In the case of exact protocols, we completely characterise one-way communication complexity for all f . We also show that, when f is monotone, g’s quantum and classical complexities are quadratically related, and that ...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2018
ISSN: 0097-5397,1095-7111
DOI: 10.1137/17m1136869