SIAM Journal on Computing
Theoretical Computer Science
Why is Boolean complexity theory difficult?
Poceedings of the London Mathematical Society symposium on Boolean function complexity
Superconcentrators of depths 2 and 3; odd levels help (rarely)
Journal of Computer and System Sciences
Boolean Circuits, Tensor Ranks, and Communication Complexity
SIAM Journal on Computing
Information Processing Letters
Note on a Lower Bound on the Linear Complexity of the Fast Fourier Transform
Journal of the ACM (JACM)
The Linear Complexity of Computation
Journal of the ACM (JACM)
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
On the rigidity of Vandermonde matrices
Theoretical Computer Science
Lower Bounds for Matrix Product in Bounded Depth Circuits with Arbitrary Gates
SIAM Journal on Computing
Superconcentrators, generalizers and generalized connectors with limited depth
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Entropy of Operators or why Matrix Multiplication is Hard for Depth-Two Circuits
Theory of Computing Systems
Lower bounds on matrix rigidity via a quantum argument
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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A completion of an m-by-n matrix A with entries in {0,1,@?} is obtained by setting all @?-entries to constants 0 and 1. A system of semi-linear equations over GF"2 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 can have more than 2^n^-^@e^@?^m^r^(^A^) solutions, where @e0 is an absolute constant and mr(A) is the smallest rank over GF"2 of a completion of A. The conjecture is related to an old problem of proving super-linear lower bounds on the size of log-depth boolean circuits computing linear operators x@?Mx. The conjecture is also a generalization of a classical question about how much larger can non-linear codes be than linear ones. We prove some special cases of the conjecture and establish some structural properties of solution sets.