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Abstract: It is proved that there is a monotone function in AC (0) 4 which requires exponential size monotone perceptrons of depth 3. This solves the monotone version of a problem which, in the general case, would imply an oracle separation of PP PH . 1 Introduction Recently perceptrons (see definition below) have received some renewed attention because of their relevance to some important issues in structural complexity theory. In [6] it was shown that perceptrons cannot compute parity unless they ... (Update)
Context of citations to this paper: More
...berg,staffanu nada.kth.se. 1 compute parity. This bound implies the existence of an oracle that separates PhiP from PP PH . Green [7] also discussed the question of whether there is an oracle that separates the levels in the PP PH hierarchy. Since this follows from a...
Cited by: More
A Lower Bound for Perceptrons and an Oracle Separation of the.. - Berg, Ulfberg (1997) (Correct)
Active bibliography (related documents): More All
0.5: On the Power of Deterministic Reductions to .. - Green (1991) (Correct)
0.1: Size-Depth Trade-offs for Threshold Circuits (Extended Abstract) - Impagliazzo, al. (Correct)
0.1: On The Power Of Small-Depth Threshold Circuits - Håstad, Goldmann (1991) (Correct)
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0.2: On the number of ANDs versus the number of ORs in monotone Boolean .. - Zwick (1996) (Correct)
0.1: Circuits Over PP and PL - Beigel, Fu (1997) (Correct)
0.1: PP is Closed Under Intersection - Beigel, Reingold, Spielman (1991) (Correct)
BibTeX entry: (Update)
Frederic Green. A lower bound for monotone perceptrons. Mathematical Systems Theory, 28:283--298, 1995. http://citeseer.ist.psu.edu/green95lower.html More
@article{ green95lower,
author = "Frederic Green",
title = "A Lower Bound for Monotone Perceptrons",
journal = "Mathematical Systems Theory",
volume = "28",
number = "4",
pages = "283-298",
year = "1995",
url = "citeseer.ist.psu.edu/green95lower.html" }
Citations (may not include all citations):77 Threshold circuits of bounded depth (context) - Hajnal, Maass et al. - 1987
68 Computational limitations for small-depth circuits (context) - Hastad - 1987
66 PP is closed under intersection - Beigel, Reingold et al. - 1991
65 A note on the power of threshold circuits (context) - Allender - 1989
56 The Expressive Power of Voting Polynomials - Aspnes, Beigel et al. - 1991
44 the computational power of PP and \PhiP (context) - Toda - 1989
27 the Power of Small-Depth Threshold Circuits (context) - Hastad, Goldmann - 1991
25 The Perceptron Strikes Back - Beigel, Reingold et al. - 1991
19 Circuits and local computation (context) - Yao - 1989
8 Perceptrons (context) - Minsky, Papert - 1988
2 Randomized Polynomials, Threshold Circuits, and the Polynomi.. (context) - Tarui - 1991
1 An oracle separating \PhiP from PP PH (context) - Green - 1991
1 Perceptrons, PP, and the Polynomial Hierarchy - Beigel - 1992
Documents on the same site (http://math-gw.clarku.edu/~fgreen/papers/papers.html): More
Exponential Sums and Circuits with a Single Threshold Gate and.. - Green (1999) (Correct)
Complex Fourier Technique for Lower Bounds on the Mod-m Degree - Green (Correct)
Quantum NP is Hard for PH - Fenner, Green, al. (1998) (Correct)
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