منابع مشابه
Min-Rank Conjecture for Log-Depth Circuits
A completion of an m-by-n matrix A with entries in {0, 1, ∗} is obtained by setting all ∗-entries to constants 0 or 1. A system of semi-linear equations over GF2 has the form Mx = f(x), where M is a completion of A and f : {0, 1}n → {0, 1}m is an operator, the ith coordinate of which can only depend on variables corresponding to ∗-entries in the ith row of A. We conjecture that no such system c...
متن کاملCommunication Complexity and the Log-rank Conjecture
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...
متن کاملThe Log-Rank Conjecture for Read- k XOR Functions
The log-rank conjecture states that the deterministic communication complexity of a Boolean function g (denoted by D(g)) is polynomially related to the logarithm of the rank of the communication matrixMg whereMg is the communication matrix defined byMg(x, y) = g(x, y). An XOR function F : {0, 1} × {0, 1} → {0, 1} with respect to f : {0, 1} → {0, 1} is a function defined by F (x, y) = f(x⊕ y). I...
متن کاملLog Depth Circuits for Division and Related Problems
We present optimal depth Boolean circuits (depth O(log n)) for integer division, powering and multiple products We also show tha t these three problems are of equivalent uniform depth and space complexity In addition, we describe an algorithm for testing drvisibility tha t is optimal for both depth and space
متن کاملSensitivity Conjecture and Log-Rank Conjecture for Functions with Small Alternating Numbers
The Sensitivity Conjecture and the Log-rank Conjecture are among the most important and challenging problems in concrete complexity. Incidentally, the Sensitivity Conjecture is known to hold for monotone functions, and so is the Log-rank Conjecture for f(x∧y) and f(x⊕y) with monotone functions f , where ∧ and ⊕ are bit-wise AND and XOR, respectively. In this paper, we extend these results to fu...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2011
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2009.09.003