메뉴 건너뛰기




Volumn 288, Issue 1, 2002, Pages 21-43

Complexity measures and decision tree complexity: A survey

Author keywords

Complexity measures for Boolean functions; Decision tree complexity; Quantum computing; Randomized computing

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; COMPUTER SCIENCE; DECISION THEORY; MATHEMATICAL MODELS; POLYNOMIAL APPROXIMATION; QUANTUM THEORY; SET THEORY; THEOREM PROVING; TREES (MATHEMATICS);

EID: 0037048579     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(01)00144-X     Document Type: Conference Paper
Times cited : (560)

References (49)
  • 1
    • 0010437727 scopus 로고    scopus 로고
    • A note on quantum black-box complexity of almost all Boolean functions
    • A. Ambainis, A note on quantum black-box complexity of almost all Boolean functions, Inform. Process. Lett. 71(1) (1999) 5-7. Also at http://arxiv.org/abs/quant-ph/9811080.
    • (1999) Inform. Process. Lett. , vol.71 , Issue.1 , pp. 5-7
    • Ambainis, A.1
  • 2
    • 84944032401 scopus 로고    scopus 로고
    • Average-case quantum query complexity
    • Proc. 17th Annu. Symp. on Theoretical Aspects of Computer Science (STACS'2000), Springer, Berlin, quant-ph/9904079
    • A. Ambainis, R. de Wolf, Average-case quantum query complexity, in: Proc. 17th Annu. Symp. on Theoretical Aspects of Computer Science (STACS'2000), Lecture Notes in Computer Science, Vol. 1770, Springer, Berlin, 2000, pp. 133-144, quant-ph/9904079.
    • (2000) Lecture Notes in Computer Science , vol.1770 , pp. 133-144
    • Ambainis, A.1    De Wolf, R.2
  • 5
    • 0010473991 scopus 로고    scopus 로고
    • Sensitivity vs. block sensitivity (an average-case study)
    • A. Bernasconi, Sensitivity vs. block sensitivity (an average-case study), Inform. Process. Lett. 59 (3) (1996) 151-157.
    • (1996) Inform. Process. Lett. , vol.59 , Issue.3 , pp. 151-157
    • Bernasconi, A.1
  • 6
    • 0023564748 scopus 로고
    • Generic oracles and oracle classes (extended abstract)
    • M. Blum, R. Impagliazzo, Generic oracles and oracle classes (extended abstract), Proc. 28th FOCS, 1987, pp. 118-126.
    • (1987) Proc. 28th FOCS , pp. 118-126
    • Blum, M.1    Impagliazzo, R.2
  • 7
    • 0031221311 scopus 로고    scopus 로고
    • The average sensitivity of bounded-depth circuits
    • R.B. Boppana, The average sensitivity of bounded-depth circuits. Inform. Proc. Lett. 63 (5) (1997) 257-261.
    • (1997) Inform. Proc. Lett. , vol.63 , Issue.5 , pp. 257-261
    • Boppana, R.B.1
  • 8
    • 0033309275 scopus 로고    scopus 로고
    • Bounds for small-error and zero-error quantum algorithms
    • cs.CC/9904019
    • H. Buhrman, R. Cleve, R. de Wolf, Ch. Zalka, Bounds for small-error and zero-error quantum algorithms. Proc. 40th FOCS, 1999, pp. 358-368, cs.CC/9904019.
    • (1999) Proc. 40th FOCS , pp. 358-368
    • Buhrman, H.1    Cleve, R.2    De Wolf, R.3    Zalka, Ch.4
  • 10
    • 0022662878 scopus 로고
    • Upper and lower time bounds for parallel random access machines without simultaneous writes
    • S. Cook, C. Dwork, R. Reischuk, Upper and lower time bounds for parallel random access machines without simultaneous writes, SIAM J. Comput. 15 (1986) 87-97.
    • (1986) SIAM J. Comput. , vol.15 , pp. 87-97
    • Cook, S.1    Dwork, C.2    Reischuk, R.3
  • 11
    • 84887490720 scopus 로고    scopus 로고
    • Space-time tradeoffs for graph properties
    • Y. Dodis, S. Khanna, Space-time tradeoffs for graph properties, Proc. 26th ICALP, 1999, pp. 291-300.
    • (1999) Proc. 26th ICALP , pp. 291-300
    • Dodis, Y.1    Khanna, S.2
  • 12
    • 0001952270 scopus 로고
    • Schwankung von polynomen zwischen gitterpunkten
    • H. Ehlich, K. Zeller, Schwankung von Polynomen zwischen Gitterpunkten, Math. Z. 86 (1964) 41-44.
    • (1964) Math. Z. , vol.86 , pp. 41-44
    • Ehlich, H.1    Zeller, K.2
  • 13
    • 0001207678 scopus 로고    scopus 로고
    • A limit on the speed of quantum computation in determining parity
    • quant-ph/9802045
    • E. Farhi, J. Goldstone, S. Gutmann, M. Sipser, A limit on the speed of quantum computation in determining parity, Phys. Rev. Lett. 81 (1998), 5442-5444, quant-ph/9802045.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 5442-5444
    • Farhi, E.1    Goldstone, J.2    Gutmann, S.3    Sipser, M.4
  • 16
    • 0032597113 scopus 로고    scopus 로고
    • Complexity limitations on quantum computation
    • Earlier version in Complexity'98, cs.CC/9811023
    • L. Fortnow, J. Rogers, Complexity limitations on quantum computation, J. Comput. Systems Sci. 59 (2) (1999) 240-252, Earlier version in Complexity'98, cs.CC/9811023.
    • (1999) J. Comput. Systems Sci. , vol.59 , Issue.2 , pp. 240-252
    • Fortnow, L.1    Rogers, J.2
  • 17
    • 0031468656 scopus 로고    scopus 로고
    • Polynomials with two values
    • J. von zur Gathen, J.R. Roche, Polynomials with two values, Combinatorica 17 (3) (1997) 345-362.
    • (1997) Combinatorica , vol.17 , Issue.3 , pp. 345-362
    • Von zur Gathen, J.1    Roche, J.R.2
  • 19
    • 0029701737 scopus 로고    scopus 로고
    • A fast quantum mechanical algorithm for database search
    • quant-ph/9605043
    • L.K. Grover, A fast quantum mechanical algorithm for database search, Proc. 28th STOC, 1996, pp. 212-219, quant-ph/9605043.
    • (1996) Proc. 28th STOC , pp. 212-219
    • Grover, L.K.1
  • 20
    • 0010475207 scopus 로고
    • 4/3 lower bound on the randomized complexity of graph properties
    • Earlier version in Structures'90
    • 4/3 lower bound on the randomized complexity of graph properties, Combinatorica 11 (1991) 131-143, Earlier version in Structures'90.
    • (1991) Combinatorica , vol.11 , pp. 131-143
    • Hajnal, P.1
  • 22
    • 38249007016 scopus 로고
    • On read-once threshold formulae and their randomized decision tree complexity
    • Earlier version in Structures'90
    • R. Heiman, I. Newman, A. Wigderson, On read-once threshold formulae and their randomized decision tree complexity, Theoret. Comput. Sci. 107 (1) (1993) 63-76, Earlier version in Structures'90.
    • (1993) Theoret. Comput. Sci. , vol.107 , Issue.1 , pp. 63-76
    • Heiman, R.1    Newman, I.2    Wigderson, A.3
  • 23
    • 0010475367 scopus 로고
    • Randomized vs. deterministic decision tree complexity for read-once Boolean functions
    • Earlier version in Structures'91
    • R. Heiman, A. Wigderson, Randomized vs. deterministic decision tree complexity for read-once Boolean functions, Comput. Complexity 1 (1991) 311-329, Earlier version in Structures'91.
    • (1991) Comput. Complexity , vol.1 , pp. 311-329
    • Heiman, R.1    Wigderson, A.2
  • 24
    • 0024140061 scopus 로고
    • The influence of variables on Boolean functions
    • J. Kahn, G. Kalai, N. Linial, The influence of variables on Boolean functions, Proc. 29th FOCS, 1988, pp. 68-80.
    • (1988) Proc. 29th FOCS , pp. 68-80
    • Kahn, J.1    Kalai, G.2    Linial, N.3
  • 25
    • 51249180724 scopus 로고
    • A topological approach to evasiveness
    • Earlier version in FOCS'83
    • J. Kahn, M. Saks, D. Sturtevant, A topological approach to evasiveness, Combinatorica 4 (1984) 297-306, Earlier version in FOCS'83.
    • (1984) Combinatorica , vol.4 , pp. 297-306
    • Kahn, J.1    Saks, M.2    Sturtevant, D.3
  • 26
    • 84898957813 scopus 로고
    • Lower bounds on the complexity of graph properties
    • V. King, Lower bounds on the complexity of graph properties, Proc. 20th STOC, 1988, pp. 468-476.
    • (1988) Proc. 20th STOC , pp. 468-476
    • King, V.1
  • 29
    • 0032633492 scopus 로고    scopus 로고
    • The quantum query complexity of approximating the median and related statistics
    • quant-ph/9804066
    • A. Nayak, F. Wu, The quantum query complexity of approximating the median and related statistics, Proc. 31st STOC, 1999, pp. 384-393, quant-ph/9804066.
    • (1999) Proc. 31st STOC , pp. 384-393
    • Nayak, A.1    Wu, F.2
  • 31
    • 0026389757 scopus 로고
    • CREW PRAMs and decision trees
    • Earlier version in STOC'89
    • N. Nisan, CREW PRAMs and decision trees, SIAM J. Comput. 20 (6) (1991) 999-1007, Earlier version in STOC'89.
    • (1991) SIAM J. Comput. , vol.20 , Issue.6 , pp. 999-1007
    • Nisan, N.1
  • 32
    • 0000607672 scopus 로고
    • On the degree of Boolean functions as real polynomials
    • Earlier version in STOC'92
    • N. Nisan, M. Szegedy, On the degree of Boolean functions as real polynomials, Comput. Complexity 4 (4) (1994) 301-313, Earlier version in STOC'92.
    • (1994) Comput. Complexity , vol.4 , Issue.4 , pp. 301-313
    • Nisan, N.1    Szegedy, M.2
  • 33
    • 21844488639 scopus 로고
    • On rank vs. communication complexity
    • Earlier version in FOCS'94
    • N. Nisan, A. Wigderson, On rank vs. communication complexity, Combinatorica 15 (4) (1995) 557-565, Earlier version in FOCS'94.
    • (1995) Combinatorica , vol.15 , Issue.4 , pp. 557-565
    • Nisan, N.1    Wigderson, A.2
  • 34
    • 0026993996 scopus 로고
    • On the degree of polynomials that approximate symmetric Boolean functions (preliminary version)
    • R. Paturi, On the degree of polynomials that approximate symmetric Boolean functions (preliminary version), Proc. 24th STOC, 1992, pp. 468-474.
    • (1992) Proc. 24th STOC , pp. 468-474
    • Paturi, R.1
  • 35
    • 0001069485 scopus 로고
    • On recognizing graph properties from adjacency matrices
    • R. Rivest, S. Vuillemin, On recognizing graph properties from adjacency matrices, Theoret. Comput. Sci. 3 (1976) 371-384.
    • (1976) Theoret. Comput. Sci. , vol.3 , pp. 371-384
    • Rivest, R.1    Vuillemin, S.2
  • 36
    • 0000977087 scopus 로고
    • A comparison of uniform approximations on an interval and a finite subset thereof
    • T.J. Rivlin, E.W. Cheney, A comparison of uniform approximations on an interval and a finite subset thereof, SIAM J. Numer. Anal. 3 (2) (1966) 311-320.
    • (1966) SIAM J. Numer. Anal. , vol.3 , Issue.2 , pp. 311-320
    • Rivlin, T.J.1    Cheney, E.W.2
  • 37
    • 0001393530 scopus 로고
    • Sensitivity vs. block sensitivity of Boolean functions
    • D. Rubinstein, Sensitivity vs. block sensitivity of Boolean functions. Combinatorica. 15 (2) (1995) 297-299.
    • (1995) Combinatorica , vol.15 , Issue.2 , pp. 297-299
    • Rubinstein, D.1
  • 38
    • 0022863767 scopus 로고
    • Probabilistic Boolean decision trees and the complexity of evaluating game trees
    • M. Saks, A. Wigderson, Probabilistic Boolean decision trees and the complexity of evaluating game trees, Proc. 27th FOCS, 1986, pp. 29-38.
    • (1986) Proc. 27th FOCS , pp. 29-38
    • Saks, M.1    Wigderson, A.2
  • 39
  • 40
    • 0034227575 scopus 로고    scopus 로고
    • Lower bounds of quantum black-box complexity and degree of approximating polynomials by influence of Boolean variables
    • quant-ph/9904107
    • Y. Shi, Lower bounds of quantum black-box complexity and degree of approximating polynomials by influence of Boolean variables, Inform. Process. Lett. 75(1-2) (2000) 79-83, quant-ph/9904107.
    • (2000) Inform. Process. Lett. , vol.75 , Issue.1-2 , pp. 79-83
    • Shi, Y.1
  • 41
    • 85012890285 scopus 로고
    • A tight Ω(loglog n)-bound on the time for parallel RAM's to compute non-degenerate Boolean functions
    • Symp. on Foundations of Computation Theory, Springer, Berlin
    • H.U. Simon, A tight Ω(loglog n)-bound on the time for parallel RAM's to compute non-degenerate Boolean functions, in: Symp. on Foundations of Computation Theory, Lecture Notes in Computer Science, Vol. 158, Springer, Berlin, 1983, pp. 439-444.
    • (1983) Lecture Notes in Computer Science , vol.158 , pp. 439-444
    • Simon, H.U.1
  • 42
    • 0022067041 scopus 로고
    • Lower bounds for probabilistic linear decision trees
    • M. Snir, Lower bounds for probabilistic linear decision trees. Theoret. Comput. Sci. 38 (1985) 69-82.
    • (1985) Theoret. Comput. Sci. , vol.38 , pp. 69-82
    • Snir, M.1
  • 43
    • 0001517258 scopus 로고
    • A by random oracles A?
    • A by random oracles A?, Combinatorica 9 (4) (1989) 385-392.
    • (1989) Combinatorica , vol.9 , Issue.4 , pp. 385-392
    • Tardos, G.1
  • 44
    • 0001527463 scopus 로고
    • The critical complexity of graph properties
    • G. Turán, The critical complexity of graph properties, Inform. Process. Lett. 18 (1984) 151-153.
    • (1984) Inform. Process. Lett. , vol.18 , pp. 151-153
    • Turán, G.1
  • 45
    • 0032313975 scopus 로고    scopus 로고
    • Quantum oracle interrogation: Getting all information for almost half the price
    • quant-ph/9805006
    • W. van Dam, Quantum oracle interrogation: Getting all information for almost half the price, Proc. 39th FOCS, 1998, pp. 362-367, quant-ph/9805006.
    • (1998) Proc. 39th FOCS , pp. 362-367
    • Van Dam, W.1
  • 46
    • 0022142015 scopus 로고
    • The critical complexity of all (monotone) Boolean functions and monotone graph properties
    • I. Wegener, The critical complexity of all (monotone) Boolean functions and monotone graph properties, Information and Control, 67 (1985) 212-222.
    • (1985) Information and Control , vol.67 , pp. 212-222
    • Wegener, I.1
  • 48
    • 0010473374 scopus 로고
    • A note on the relations between critical and sensitive complexity
    • I. Wegener, L. Zádori, A note on the relations between critical and sensitive complexity, J. Inform. Process. Cybernet. (EIK). 25 (8/9) (1989) 417-421.
    • (1989) J. Inform. Process. Cybernet. (EIK) , vol.25 , Issue.8-9 , pp. 417-421
    • Wegener, I.1    Zádori, L.2
  • 49
    • 0033700248 scopus 로고    scopus 로고
    • Characterization of non-deterministic quantum query and quantum communication complexity
    • cs.CC/0001014
    • R. de Wolf, Characterization of non-deterministic quantum query and quantum communication complexity, Proc. 15th IEEE Conf. on Computational Complexity, 2000, pp. 271-278, cs.CC/0001014.
    • (2000) Proc. 15th IEEE Conf. on Computational Complexity , pp. 271-278
    • De Wolf, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.