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Volumn 56, Issue 3, 1998, Pages 263-271

A Lower Bound for Perceptrons and an Oracle Separation of the PPPH Hierarchy

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; NEURAL NETWORKS; POLYNOMIALS;

EID: 0032090473     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1997.1552     Document Type: Article
Times cited : (7)

References (14)
  • 1
    • 0038384210 scopus 로고
    • Perceptions, PP, and the polynomial hierarchy
    • R. Beigel, Perceptions, PP, and the polynomial hierarchy, Comput. Complexity 4, No. 4 (1994), 339-349.
    • (1994) Comput. Complexity , vol.4 , Issue.4 , pp. 339-349
    • Beigel, R.1
  • 2
    • 0025791380 scopus 로고
    • Probabilistic polynomial time is closed under parity reductions
    • R. Beigel, L. A. Hemachandra, and G. Wechsung, Probabilistic polynomial time is closed under parity reductions, Inform. Process. Lett. 37 (1991), 91-94.
    • (1991) Inform. Process. Lett. , vol.37 , pp. 91-94
    • Beigel, R.1    Hemachandra, L.A.2    Wechsung, G.3
  • 4
    • 51249163193 scopus 로고
    • Separating PH from PP by relativization
    • B. Fu, Separating PH from PP by relativization, Acta Math. Sinica (New Ser.) 8, No. 3 (1992), 329-336.
    • (1992) Acta Math. Sinica (New Ser.) , vol.8 , Issue.3 , pp. 329-336
    • Fu, B.1
  • 5
    • 0002127588 scopus 로고
    • Parity, circuits, and the polynomial-time hierarchy
    • M. Furst, J. B. Saxe, and M. Sipser, Parity, circuits, and the polynomial-time hierarchy, Math. Systems Theory 17 (1984), 13-27.
    • (1984) Math. Systems Theory , vol.17 , pp. 13-27
    • Furst, M.1    Saxe, J.B.2    Sipser, M.3
  • 7
    • 0347388993 scopus 로고
    • A lower bound for monotone perceptrons
    • F. Green, A lower bound for monotone perceptrons, Math. Systems Theory 28 (1995), 283-298.
    • (1995) Math. Systems Theory , vol.28 , pp. 283-298
    • Green, F.1
  • 9
    • 0002343638 scopus 로고
    • Almost optimal lower bounds for small depth circuits
    • "Randomness and Computation" (S. Micali, Ed.), JAI Press, London
    • J. Håstad, Almost optimal lower bounds for small depth circuits, in "Randomness and Computation" (S. Micali, Ed.), Advances in Computing Research, Vol. 5, pp. 143-170, JAI Press, London, 1989.
    • (1989) Advances in Computing Research , vol.5 , pp. 143-170
    • Håstad, J.1
  • 10
    • 0001295178 scopus 로고
    • On the power of small-depth threshold circuits
    • J. Håstad and M. Goldmann, On the power of small-depth threshold circuits, Comput. Complexity 1, No. 2 (1991), 113-129.
    • (1991) Comput. Complexity , vol.1 , Issue.2 , pp. 113-129
    • Håstad, J.1    Goldmann, M.2
  • 11
    • 0024646217 scopus 로고
    • Relativized polynomial time hierarchies having exactly k levels
    • K. Ko, Relativized polynomial time hierarchies having exactly k levels, SIAM J. Comput. 18, No. 2 (1989), 392-408.
    • (1989) SIAM J. Comput. , vol.18 , Issue.2 , pp. 392-408
    • Ko, K.1
  • 12
    • 0004290881 scopus 로고
    • MIT Press, Cambridge, MA, expanded edition
    • M. Minsky and S. Papert, "Perceptrons," MIT Press, Cambridge, MA, 1988. [expanded edition]
    • (1988) Perceptrons
    • Minsky, M.1    Papert, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.