메뉴 건너뛰기




Volumn 19, Issue 2, 2010, Pages 211-234

A new characterization of ACC0 and probabilistic CC0

Author keywords

AND function; Boolean circuits; Branching programs; Modular counting; Planarity; Probabilistic circuits

Indexed keywords


EID: 77953538534     PISSN: 10163328     EISSN: 14208954     Source Type: Journal    
DOI: 10.1007/s00037-010-0287-z     Document Type: Article
Times cited : (14)

References (52)
  • 2
    • 0042419955 scopus 로고
    • Approximate counting with uniform constant depth circuits
    • J.-Y Cai, editor, volume 13 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society
    • M. Ajtai (1993). Approximate counting with uniform constant depth circuits. In Advances in Computational Complexity Theory, J.-Y Cai, editor, volume 13 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1-20. American Mathematical Society.
    • (1993) In Advances In Computational Complexity Theory , pp. 1-20
    • Ajtai, M.1
  • 5
    • 0008651743 scopus 로고
    • Depth reduction for circuits of unbounded fan-in
    • E. Allender & U. Hertrampf (1994). Depth reduction for circuits of unbounded fan-in. Information and Computation 112(2), 217-238.
    • (1994) Information and Computation , vol.112 , Issue.2 , pp. 217-238
    • Allender, E.1    Hertrampf, U.2
  • 6
    • 0002507290 scopus 로고    scopus 로고
    • Non-Commutative arithmetic circuits: Depth reduction and size lower bounds
    • E. Allender, J. Jiao, M. Mahajan & V. Vinay (1998). Non-Commutative arithmetic circuits: depth reduction and size lower bounds. Theoretical Computer Science 209(1-2), 47-86.
    • (1998) Theoretical Computer Science , vol.209 , Issue.1-2 , pp. 47-86
    • Allender, E.1    Jiao, J.2    Mahajan, M.3    Vinay, V.4
  • 9
    • 0003430191 scopus 로고    scopus 로고
    • John Wiley & Sons, 2nd edition. ISBN 0-471-37046-0
    • N. Alon & J. Spencer (2000). The Probabilistic Method. John Wiley & Sons, 2nd edition. ISBN 0-471-37046-0.
    • (2000) The Probabilistic Method
    • Alon, N.1    Spencer, J.2
  • 12
    • 0041120667 scopus 로고
    • Some problems involving Razborov-Smolensky polynomials
    • M. S. Paterson, editor, volume 169 of London Mathematical Society Lecture Note Series, Cambridge University Press
    • D. A. Mix Barrington (1992). Some problems involving Razborov-Smolensky polynomials. In Boolean Function Complexity, M. S. Paterson, editor, volume 169 of London Mathematical Society Lecture Note Series, 109-128. Cambridge University Press.
    • (1992) In Boolean Function Complexity , pp. 109-128
    • Mix Barrington, D.A.1
  • 13
    • 0000107258 scopus 로고
    • Representing Boolean functions as polynomials modulo composite numbers
    • D. A. Mix Barrington, R. Beigel & S. Rudich (1994). Representing Boolean functions as polynomials modulo composite numbers. computational complexity 4, 367-382.
    • (1994) Computational Complexity , vol.4 , pp. 367-382
    • Mix Barrington, D.A.1    Beigel, R.2    Rudich, S.3
  • 21
    • 13544277865 scopus 로고    scopus 로고
    • A note on a theorem of Barrington, Straubing and Thérien
    • H. Caussinus (1996). A note on a theorem of Barrington, Straubing and Thérien. Information Processing Letters 58(1), 31-33.
    • (1996) Information Processing Letters , vol.58 , Issue.1 , pp. 31-33
    • Caussinus, H.1
  • 24
    • 0002127588 scopus 로고
    • Parity, circuits, and the polynomialtime hierarchy
    • M. Furst, J. B. Saxe & M. Sipser (1984). Parity, circuits, and the polynomialtime hierarchy. Mathematical Systems Theory 17(1), 13-27.
    • (1984) Mathematical Systems Theory , vol.17 , Issue.1 , pp. 13-27
    • Furst, M.1    Saxe, J.B.2    Sipser, M.3
  • 25
    • 0000871697 scopus 로고
    • Explicit constructions of linear-sized superconcentrators
    • O. Gabber & Z. Galil (1981). Explicit constructions of linear-sized superconcentrators. Journal of Computer and System Sciences 22(3), 407-420.
    • (1981) Journal of Computer and System Sciences , vol.22 , Issue.3 , pp. 407-420
    • Gabber, O.1    Galil, Z.2
  • 26
    • 0034363403 scopus 로고    scopus 로고
    • Superpolynomial size set-systems with restricted intersections mod 6 and explicit Ramsey graphs
    • V. Grolmusz (2000). Superpolynomial size set-systems with restricted intersections mod 6 and explicit Ramsey graphs. Combinatorica 20(1), 71-86.
    • (2000) Combinatorica , vol.20 , Issue.1 , pp. 71-86
    • Grolmusz, V.1
  • 34
    • 70349496554 scopus 로고    scopus 로고
    • Circuit complexity of regular languages
    • M. Koucký (2009). Circuit complexity of regular languages. Theory of Computing Systems 45(4), 865-879.
    • (2009) Theory of Computing Systems , vol.45 , Issue.4 , pp. 865-879
    • Koucký, M.1
  • 36
    • 0043276850 scopus 로고
    • Variation ranks of communication matrices and lower bounds for depth-two circuits having nearly symmetric gates with unbounded fan-in
    • M. Krause & S. Waack (1995). Variation ranks of communication matrices and lower bounds for depth-two circuits having nearly symmetric gates with unbounded fan-in. Mathematical Systems Theory 28(6), 553-564.
    • (1995) Mathematical Systems Theory , vol.28 , Issue.6 , pp. 553-564
    • Krause, M.1    Waack, S.2
  • 37
    • 0021098038 scopus 로고
    • BPP and the polynomial hierarchy
    • C. Lautemann (1983). BPP and the polynomial hierarchy. Information Processing Letters 17(4), 215-217.
    • (1983) Information Processing Letters , vol.17 , Issue.4 , pp. 215-217
    • Lautemann, C.1
  • 38
    • 0000789645 scopus 로고
    • Explicit constructions of expanders
    • G. A. Margulis (1973). Explicit constructions of expanders. Problemy Peredači Informacii 9(4), 71-80.
    • (1973) Problemy Peredači Informacii , vol.9 , Issue.4 , pp. 71-80
    • Margulis, G.A.1
  • 39
    • 0000947929 scopus 로고
    • Pseudorandom generators for space-bounded computation
    • N. Nisan (1992). Pseudorandom generators for space-bounded computation. Combinatorica 12(4), 449-461.
    • (1992) Combinatorica , vol.12 , Issue.4 , pp. 449-461
    • Nisan, N.1
  • 40
    • 26944478724 scopus 로고
    • Lower bounds for the size of circuits of bounded depth with basis (∧, ⊕)
    • A. A. Razborov (1987). Lower bounds for the size of circuits of bounded depth with basis (∧, ⊕). Mathematical Notes of the Academy of Science of the USSR 41(4), 333-338.
    • (1987) Mathematical Notes of The Academy of Science of The USSR , vol.41 , Issue.4 , pp. 333-338
    • Razborov, A.A.1
  • 43
    • 0025554840 scopus 로고
    • On interpolation by analytic functions with special properties and some weak lower bounds on the size of circuits with symmetric gates
    • St. Louis MO, IEEE Computer Society Press
    • R. Smolensky (1990). On interpolation by analytic functions with special properties and some weak lower bounds on the size of circuits with symmetric gates. In Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science, St. Louis MO, 628-631. IEEE Computer Society Press.
    • (1990) In Proceedings of The 31st Annual IEEE Symposium On Foundations of Computer Science , pp. 628-631
    • Smolensky, R.1
  • 46
    • 0027591463 scopus 로고
    • 0 functions and the polynomial-time hierarchy
    • 0 functions and the polynomial-time hierarchy. Theoretical Computer Science 113(1), 167-183.
    • (1993) Theoretical Computer Science , vol.113 , Issue.1 , pp. 167-183
    • Tarui, J.1
  • 47
    • 4244118786 scopus 로고
    • q gates cannot compute And in sublinear size
    • D. Thérien (1994). Circuits constructed with MODq gates cannot compute And in sublinear size. computational complexity 4, 383-388.
    • (1994) Computational Complexity , vol.4 , pp. 383-388
    • Thérien, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.