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Volumn 32, Issue 4, 1999, Pages 453-466

Exponential sums and circuits with a single threshold gate and mod-gates

Author keywords

[No Author keywords available]

Indexed keywords

EXPONENTIAL FUNCTIONS; THRESHOLD ELEMENTS; TIMING CIRCUITS;

EID: 0033417012     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s002240000126     Document Type: Article
Times cited : (10)

References (24)
  • 4
    • 0000107258 scopus 로고
    • Representing Boolean functions as polynomials modulo composite numbers
    • D. A. M. Barrington, R. Beigel, and S. Rudich, Representing Boolean functions as polynomials modulo composite numbers, Computational Complexity, 4 (1994), 367-382.
    • (1994) Computational Complexity , vol.4 , pp. 367-382
    • Barrington, D.A.M.1    Beigel, R.2    Rudich, S.3
  • 6
    • 0024606088 scopus 로고
    • With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy
    • J.-Y. Cai, With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy, Journal of Computer and System Science, 38 (1989), 68-85.
    • (1989) Journal of Computer and System Science , vol.38 , pp. 68-85
    • Cai, J.-Y.1
  • 8
    • 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. Mathematical Systems Theory, 17 (1984), 13-27.
    • (1984) Mathematical Systems Theory , vol.17 , pp. 13-27
    • Furst, M.1    Saxe, J.B.2    Sipser, M.3
  • 10
    • 0000632542 scopus 로고
    • A note on the power of majority gates and modular gates
    • M. Goldmann, A note on the power of majority gates and modular gates, Information Processing Letter, 53 (1995), 321-327.
    • (1995) Information Processing Letter , vol.53 , pp. 321-327
    • Goldmann, M.1
  • 13
    • 0001295178 scopus 로고
    • On the power of small-depth threshold circuits
    • J. Håstad and M. Goldmann, On the power of small-depth threshold circuits, Computational Complexity, 1 (1991), 113-129.
    • (1991) Computational Complexity , vol.1 , pp. 113-129
    • Håstad, J.1    Goldmann, M.2
  • 15
    • 0000400921 scopus 로고
    • Sommes exponentielles
    • N. Katz, Sommes exponentielles, Astérisque, 79 (1980).
    • (1980) Astérisque , vol.79
    • Katz, N.1
  • 18
    • 0000883554 scopus 로고
    • Lower bounds on the size of bounded depth networks over a complete basis with logical addition
    • A. A. Razborov, Lower bounds on the size of bounded depth networks over a complete basis with logical addition, Matematicheskie Zametki, 41 (1987), 598-607. English translation in Mathematical Notes of the Academy of Sciences of the USSK, 41 (1987), 333-338.
    • (1987) Matematicheskie Zametki , vol.41 , pp. 598-607
    • Razborov, A.A.1
  • 19
    • 26944478724 scopus 로고
    • English translation in
    • A. A. Razborov, Lower bounds on the size of bounded depth networks over a complete basis with logical addition, Matematicheskie Zametki, 41 (1987), 598-607. English translation in Mathematical Notes of the Academy of Sciences of the USSK, 41 (1987), 333-338.
    • (1987) Mathematical Notes of the Academy of Sciences of the USSK , vol.41 , pp. 333-338
  • 20
    • 0003215121 scopus 로고
    • Equations over Finite Fields: An Elementary Approach
    • Springer-Verlag, New York
    • W. M. Schmidt, Equations over Finite Fields: An Elementary Approach, Lecture Notes in Mathematics, vol. 536, Springer-Verlag, New York, 1976.
    • (1976) Lecture Notes in Mathematics , vol.536
    • Schmidt, W.M.1
  • 22
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    • PP is as hard as the polynomial-time hierarchy
    • S. Toda, PP is as hard as the polynomial-time hierarchy, SIAM Journal on Computing, 20 (1991), 865-877.
    • (1991) SIAM Journal on Computing , vol.20 , pp. 865-877
    • Toda, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.