The corruption bound, log-rank, and communication complexity
نویسندگان
چکیده
منابع مشابه
The Corruption Bound, Log Rank, and Communication Complexity
We prove that for every sign matrix A there is a deterministic communication protocol that uses O(corr1/4(A) log 2 rank(A)) bits of communication, where corr1/4(A) is the corruption/rectangle bound with error 1/4. This bound generalizes several of the known upper bounds on deterministic communication complexity, involving nondeterministic complexity, randomized complexity, information complexit...
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Def: A deterministic protocol computing a function f(x, y) is a binary tree T whose internal nodes specify which party speaks and the value of the bit they communicate, as a function of their input. The leaves of the tree are labelled with 0 or 1, in such a way that if Alice and Bob’s path through the tree given inputs (x, y) ends up in that leaf, the label on the leaf is f(x, y). The cost of s...
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The log-rank conjecture is one of the fundamental open problems in communication complexity. It speculates that the deterministic communication complexity of any two-party function is equal to the log of the rank of its associated matrix, up to polynomial factors. Despite much research, we still know very little about this conjecture. Recently, there has been renewed interest in this conjecture...
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We show the existence of a non{constant gap between the communication complexity of a function and the logarithm of the rank of its input matrix. We consider the following problem: each of two players gets a perfect matching between two n{element sets of vertices. Their goal is to decide whether or not the union of the two matchings forms a Hamiltonian cycle. We prove: 1) The rank of the input ...
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For a {0, 1}-valued matrixM let CC(M) denote the deterministic communication complexity of the boolean function associated with M . The log-rank conjecture of Lovász and Saks [FOCS 1988] states that CC(M) ≤ logc(rank(M)) for some absolute constant c where rank(M) denotes the rank of M over the field of real numbers. We show that CC(M) ≤ c · rank(M)/ log rank(M) for some absolute constant c, ass...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2019
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2018.09.004