A Lower Bound For Perceptrons And An Oracle Separation Of The PP/sup PH/ Hierarchy

Authors:
C. Berg;S. Ulfberg
Affiliations:
-;-
Venue:
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Year:
1997

Citing 7
Cited 0

Computational limitations of small-depth circuits

Computational limitations of small-depth circuits
Relativized polynomial time hierarchies having exactly K levels

SIAM Journal on Computing
An oracle separating ⊕ P from PPPH

Information Processing Letters
Probabilistic polynomial time is closed under parity reductions

Information Processing Letters
PP is closed under intersection

Selected papers of the 23rd annual ACM symposium on Theory of computing
Borel sets and circuit complexity

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Separating the polynomial-time hierarchy by oracles

SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science

Quantified Score

Hi-index	0.01

Visualization

Abstract

We show that there are functions computable by linear size boolean circuits of depth k that require superpolynomial size perceptrons of depth k-1, for k(6 log log n). This result implies the existence of an oracle A such that /spl Sigma//sub k//sup p,A//spl nsub/PP/sup /spl Sigma//(/sub k-2//sup p,A/) and in particular this oracle separates the levels in the PP/sup PH/ hierarchy. Using the same ideas, we show a lower bound for another function, which makes it possible to strengthen the oracle separation to /spl Delta//sub k//sup p,A//spl nsub/PP/sup /spl Sigma//(/sub k-2//sup p,A/).