메뉴 건너뛰기




Volumn 207, Issue 1, 1998, Pages 159-170

Relating polynomial time to constant depth

Author keywords

Boolean circuits; Constant depth circuits; Oracle separations; Polynomial time classes; Turing machines

Indexed keywords


EID: 0345767121     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00061-9     Document Type: Article
Times cited : (5)

References (35)
  • 1
    • 0008651743 scopus 로고
    • Depth reduction for circuits of unbounded fan-in
    • E. Allender, U. Hertrampf, Depth reduction for circuits of unbounded fan-in, Inform. and Comput. 112 (1994) 217-238.
    • (1994) Inform. and Comput. , vol.112 , pp. 217-238
    • Allender, E.1    Hertrampf, U.2
  • 4
    • 0027036709 scopus 로고
    • Quasipolynomial size circuit classes
    • IEEE Computer Society Press, Silver Spring, MD
    • D.A.M. Barrington, Quasipolynomial size circuit classes, in: Proc. 7th Structure in Complexity Theory, IEEE Computer Society Press, Silver Spring, MD, 1992, 86-93.
    • (1992) Proc. 7th Structure in Complexity Theory , pp. 86-93
    • Barrington, D.A.M.1
  • 5
    • 0004140326 scopus 로고    scopus 로고
    • Time, hardware, and uniformity
    • L.A. Hemaspaandra, A. Selman (Eds.), Springer, New York
    • D.A.M. Barrington, N. Immerman, Time, hardware, and uniformity, in: L.A. Hemaspaandra, A. Selman (Eds.), Complexity Theory Retrospective II, Springer, New York, 1997, pp. 1-22.
    • (1997) Complexity Theory Retrospective , vol.2 , pp. 1-22
    • Barrington, D.A.M.1    Immerman, N.2
  • 7
    • 0027204515 scopus 로고
    • The polynomial method in circuit complexity
    • IEEE Computer Society Press, Silver Spring, MD, 1993. Revised version
    • R. Beigel, The polynomial method in circuit complexity, in: Proc. 8th Structure in Complexity Theory, IEEE Computer Society Press, Silver Spring, MD, 1993. Revised version, 1995, pp. 82-95.
    • (1995) Proc. 8th Structure in Complexity Theory , pp. 82-95
    • Beigel, R.1
  • 8
    • 0038384210 scopus 로고
    • Perceptrons, PP, and the polynomial hierarchy
    • R. Beigel, Perceptrons, PP, and the polynomial hierarchy, Comput. Complexity 4 (1994) 339-349.
    • (1994) Comput. Complexity , vol.4 , pp. 339-349
    • Beigel, R.1
  • 10
    • 0000392346 scopus 로고
    • The complexity of finite functions
    • J. van Leeuwen (Ed.), Elsevier, Amsterdam
    • R.B. Boppana, M. Sipser, The complexity of finite functions, in: J. van Leeuwen (Ed.), Handbook of Theoretical Computer Science, vol. A, Elsevier, Amsterdam, 1990, pp. 757-804.
    • (1990) Handbook of Theoretical Computer Science , vol.A , pp. 757-804
    • Boppana, R.B.1    Sipser, M.2
  • 11
    • 0348037105 scopus 로고    scopus 로고
    • The general notion of a dot operator
    • IEEE Computer Society Press, Silver Spring, MD
    • B. Borchert, R. Silvestri, The general notion of a dot operator, in: Proc. 12th Conf. on Computational Complexity, IEEE Computer Society Press, Silver Spring, MD, 1997, pp. 26-44.
    • (1997) Proc. 12th Conf. on Computational Complexity , pp. 26-44
    • Borchert, B.1    Silvestri, R.2
  • 14
    • 0002229646 scopus 로고    scopus 로고
    • Counting complexity
    • L.A. Hemaspaandra, A. Selman (Eds), Springer, New York
    • L. Fortnow, Counting complexity, in: L.A. Hemaspaandra, A. Selman (Eds), Complexity Theory Retrospective II, Springer, New York, 1997, pp. 81-107.
    • (1997) Complexity Theory Retrospective , vol.2 , pp. 81-107
    • Fortnow, L.1
  • 15
    • 0002127588 scopus 로고
    • Parity, circuits, and the polynomial-time hierarchy
    • M. Furst, J.B. Saxe, 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
  • 16
    • 0022722612 scopus 로고
    • On the construction of parallel computers from various bases of boolean functions
    • L.M. Goldschlager, I. Parberry, On the construction of parallel computers from various bases of boolean functions, Theoret. Comput. Sci. 43 (1986) 43-58.
    • (1986) Theoret. Comput. Sci. , vol.43 , pp. 43-58
    • Goldschlager, L.M.1    Parberry, I.2
  • 22
    • 0024646217 scopus 로고
    • Relativized polynomial time hierarchies having exactly k levels
    • K.-I. Ko, Relativized polynomial time hierarchies having exactly k levels, SIAM Journal on Computing, 18 (1989) 392-408.
    • (1989) SIAM Journal on Computing , vol.18 , pp. 392-408
    • Ko, K.-I.1
  • 23
    • 84904339233 scopus 로고
    • 0 for free
    • Proc. 10th Symp. on Theoretical Aspects of Computer Science, Springer, Berlin
    • 0 for free, in: Proc. 10th Symp. on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 665, Springer, Berlin, 1993, pp. 545-554.
    • (1993) Lecture Notes in Computer Science , vol.665 , pp. 545-554
    • Maciel, A.1    Thérien, T.2
  • 25
    • 0343851485 scopus 로고    scopus 로고
    • Polynomials and combinatorial definitions of languages
    • L.A. Hemaspaandra, A.L. Selman (Eds), Springer, Berlin
    • K. Regan, Polynomials and combinatorial definitions of languages, in: L.A. Hemaspaandra, A.L. Selman (Eds), Complexity Theory Retrospective II, Springer, Berlin, 1997, pp. 261-293.
    • (1997) Complexity Theory Retrospective , vol.2 , pp. 261-293
    • Regan, K.1
  • 26
    • 0031272607 scopus 로고    scopus 로고
    • Gap-languages and log-time complexity classes
    • to appear
    • K. Regan, H. Vollmer, Gap-languages and log-time complexity classes, Theoret. Comput. Sci. (1997), to appear.
    • (1997) Theoret. Comput. Sci.
    • Regan, K.1    Vollmer, H.2
  • 27
    • 44649167785 scopus 로고    scopus 로고
    • The polynomial-time hierarchy
    • L. Stockmeyer, The polynomial-time hierarchy, Theoret. Comput. Sci. 3 (1997) 1-22.
    • (1997) Theoret. Comput. Sci. , vol.3 , pp. 1-22
    • Stockmeyer, L.1
  • 28
    • 0026239342 scopus 로고
    • PP is as hard as the polynomial time hierarchy
    • S. Toda, PP is as hard as the polynomial time hierarchy, SIAM J. Computing 20 (1991) 865-877.
    • (1991) SIAM J. Computing , vol.20 , pp. 865-877
    • Toda, S.1
  • 29
    • 0026879923 scopus 로고
    • Polynomial time 1-Turing reductions from #ph to #p
    • S. Toda, O. Watanabe, Polynomial time 1-Turing reductions from #ph to #p, Theoret. Comput. Sci. 100 (1992) 205-221.
    • (1992) Theoret. Comput. Sci. , vol.100 , pp. 205-221
    • Toda, S.1    Watanabe, O.2
  • 30
    • 0010585016 scopus 로고
    • Relativizable and non-relativizable theorems in the polynomial theory of algorithms
    • in Russian.
    • N.K. Vereshchagin, Relativizable and non-relativizable theorems in the polynomial theory of algorithms, Izvestija Rossijskoj Akademii Nauk, 57 (1993) 51-90 (in Russian).
    • (1993) Izvestija Rossijskoj Akademii Nauk , vol.57 , pp. 51-90
    • Vereshchagin, N.K.1
  • 31
    • 21344483574 scopus 로고
    • On different reducibility notions for function classes
    • Proc. 11th Symp. on Theoretical Aspects of Computer Science, Springer, Berlin
    • H. Vollmer, On different reducibility notions for function classes, in: Proc. 11th Symp. on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 775, Springer, Berlin, 1994, pp. 449-460.
    • (1994) Lecture Notes in Computer Science , vol.775 , pp. 449-460
    • Vollmer, H.1
  • 32
    • 21444447392 scopus 로고    scopus 로고
    • Relations among parallel and sequential computation models
    • Proc. 2nd Asian Computing Science Conference, Springer, Berlin
    • H. Vollmer. Relations among parallel and sequential computation models, in: Proc. 2nd Asian Computing Science Conference, Lecture Notes in Computer Science, vol. 1179, Springer, Berlin, 1996, pp. 23-32.
    • (1996) Lecture Notes in Computer Science , vol.1179 , pp. 23-32
    • Vollmer, H.1
  • 34
    • 0025507099 scopus 로고
    • Bounded query classes
    • K.W. Wagner, Bounded query classes, SIAM J. on Computing 19 (1990) 833-846.
    • (1990) SIAM J. on Computing , vol.19 , pp. 833-846
    • Wagner, K.W.1
  • 35
    • 0022201594 scopus 로고
    • Separating the polynomial-time hierarchy by oracles
    • IEEE Computer Society Press, Silver Spring
    • A.C.C. Yao, Separating the polynomial-time hierarchy by oracles, in: Proc. 26th Foundations of Computer Science, IEEE Computer Society Press, Silver Spring, 1985, pp. 1-10.
    • (1985) Proc. 26th Foundations of Computer Science , pp. 1-10
    • Yao, A.C.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.