Questions tagged [matrix-product]

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59
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4answers
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Evidence that matrix multiplication can be done in quadratic time?

It is widely conjectured that $\omega$, the optimal exponent for matrix multiplication, is in fact equal to 2. My question is simple: What reasons do we have for believing that $\omega = 2$? I'm ...
18
votes
1answer
608 views

What is the most general structure on which matrix product verification can be done in $O(n^2)$ time?

In 1979, Freivalds showed that verifying matrix products over any field can be done in randomized $O(n^2)$ time. More formally, given three matrices A, B, and C, with entries from a field F, the ...
16
votes
1answer
412 views

smallest circuit size using XOR gates

Suppose we are given a set of n boolean variables x_1,...,x_n and a set of m functions y_1...y_m where each y_i is the XOR of a (given) subset of these variables. The goal is to compute the minimum ...