Open Access
Almost Optimal Lower Bounds for Small Depth Circuits.
Johan Håstad
- Vol. 5, pp 143-170
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The article was published on 1989-01-01 and is currently open access. It has received 662 citations till now. The article focuses on the topics: Upper and lower bounds.read more
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References
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Proceedings ArticleDOI
Parity, circuits, and the polynomial-time hierarchy
TL;DR: A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function and connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.
Book
Computational limitations of small-depth circuits
TL;DR: The techniques described in "Computational Limitations for Small Depth Circuits" can be used to demonstrate almost optimal lower bounds on the size of small depth circuits computing several different functions, such as parity and majority.
Proceedings ArticleDOI
Separating the polynomial-time hierarchy by oracles
TL;DR: In this paper, the size of depth-k Boolean circuits for computing certain functions is shown to be polynomial in the number of levels in the hierarchy of the hierarchy, i.e., ΣkP,A is properly contained in Σp+1P+A for all k.
Journal ArticleDOI
The monotone circuit complexity of Boolean functions
TL;DR: The arguments of Razborov are modified to obtain exponential lower bounds for circuits, and the best lower bound for an NP function ofn variables is exp (Ω(n1/4 · (logn)1/2)), improving a recent result of exp ( Ω( n1/8-ε)) due to Andreev.