Communication complexities of symmetric XOR functions
نویسندگان
چکیده
منابع مشابه
Communication complexities of symmetric 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 ...
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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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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We study the communication complexity of symmetric XOR functions, namely functions f : {0, 1}×{0, 1} → {0, 1} that can be formulated as f(x, y) = D(|x⊕ y|) for some predicate D : {0, 1, ..., n} → {0, 1}, where |x⊕ y| is the Hamming weight of the bitwise XOR of x and y. We give a public-coin randomized protocol in the Simultaneous Message Passing (SMP) model, with the communication cost matching...
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ژورنال
عنوان ژورنال: Quantum Information and Computation
سال: 2009
ISSN: 1533-7146,1533-7146
DOI: 10.26421/qic9.3-4-5