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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 6, Pages 3–24 (Mi izv50)  

Oracle separation of complexity classes and lower bounds for perceptrons solving separation problems

N. K. Vereshchagin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In the first part of the paper we prove that, relative to a random oracle, the class NP contains infinite sets having no infinite Co-NP-subsets (Co-NP-immune sets). In the second part we prove that perceptrons separating Boolean matrices in which each row contains at least one 1 from matrices in which many rows (say 99% of them) have no 1's must have either large size or large order. This result partially strengthens the “one-in-a-box” theorem of Minsky and Papert [16] which states that perceptrons of small order cannot decide if every row of a given Boolean matrix has a 1. As a corollary, we prove that $AM\capCo-AM\not\subseteqPP$ under some oracles.

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English version:
Izvestiya: Mathematics, 1995, 59:6, 1103–1122

Bibliographic databases:

MSC: 68Q15
Received: 28.11.1994
Revised: 22.02.1995

Citation: N. K. Vereshchagin, “Oracle separation of complexity classes and lower bounds for perceptrons solving separation problems”, Izv. RAN. Ser. Mat., 59:6 (1995), 3–24; Izv. Math., 59:6 (1995), 1103–1122

Citation in format AMSBIB
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\by N.~K.~Vereshchagin
\paper Oracle separation of complexity classes and lower bounds for perceptrons solving separation problems
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 6
\pages 3--24
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\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 6
\pages 1103--1122
\crossref{https://doi.org/10.1070/IM1995v059n06ABEH000050}
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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