Oracle separation of complexity classes and lower bonnets for perceptions solving separation problems

摘要

In the first part of the paper we prove that, relative to a random oracle, the cl"s NP cantatas infinite sets having no mfinite GoNP-mibsots (Co-NP-immune sets) In the swmid part we prove that perceptrona separating Boolean matrices in which each niw contains o Jt one 1 from matrices in which many rows (say 99% of them) liavt? ao V& auutt h"ve either targe am or large order. This result partially strengthetjj the "anft-in-a-bex" th"6ram of M husky and Popart [1G] which states that perceptrons of niaall ordw cannot decide if every row of a given Boolean matrix has a 1. As a corollary, Wi prove that AM H Co-AM g PP.under some oracles.