A Lower Bound for Perceptrons and an Oracle Separation of the PPPHHierarchy
Christer Berg,Staffan Ulfberg +1 more
TLDR
In this paper, it was shown that there are functions computable by linear size boolean circuits of depth k that require superpolynomial size perceptrons of depthk?1, forkAbout:
This article is published in Journal of Computer and System Sciences.The article was published on 1998-06-01 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Boolean circuit & Fork (system call).read more
Citations
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Journal ArticleDOI
Learning DNF in time 2 õ ( n 1/3 )
TL;DR: Using techniques from learning theory, this article showed that any s-term DNF over n variables can be computed by a polynomial threshold function of degree O(n 1/3 log s).
Journal Article
Pseudorandom Bits for Constant-Depth Circuits with Few Arbitrary Symmetric Gates
TL;DR: In particular, Babai, Nisan, and Wigderson as discussed by the authors showed that any function computable by uniform poly(n)$-size probabilistic constant-depth circuits with O(log n)$ arbitrary symmetric gates can be computed in time O(2 n−n−o(1) ) with constant-time communication complexity.
Proceedings ArticleDOI
Multiparty Communication Complexity and Threshold Circuit Size of AC^0
Paul Beame,Dang-Trinh Huynh-Ngoc +1 more
TL;DR: In this paper, it was shown that the randomized k-party communication complexity of depth 4 AC^0 functions in the number-on-forehead (NOF) model for up to Theta(log n) players can be reduced to O(log log n) for non-constant k. This lower bound implies the first super polynomial lower bounds for the simulation of AC-0 by MAJ-SYMM-AND circuits.
Book ChapterDOI
Some meet-in-the-middle circuit lower bounds
TL;DR: It is observed that a combination of known top-down and bottom-up lower bound techniques of circuit complexity may yield new circuit lower bounds.
Journal Article
Some meet-in-the-middle circuit lower bounds
TL;DR: In this article, a combination of known top-down and bottom-up lower bound techniques of circuit complexity may yield new circuit lower bounds, and a simple combination of their result with the Hastad switching lemma yields the following seemingly much stronger result: the same function f in ACC° cannot be computed by polynomial size circuits consisting of two layers of MAJORITY gates at the top and an arbitrary AC 0 circuit feeding the main gates.
References
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Journal 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.
Proceedings Article
Separating the Polynomial-Time Hierarchy by Oracles (Preliminary Version)
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.