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Abstract: We discuss several complexity measures for Boolean functions: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial. We survey the relations and biggest gaps known between these measures, and show how they give bounds for the decision tree complexity of Boolean functions on deterministic, randomized, and quantum computers. 1 Introduction Computational Complexity is the subfield of Theoretical Computer Science that aims to understand ... (Update)
Context of citations to this paper: More
...model for probabilistic sampling algorithms that compute approximate solutions. This model is based on the decision tree model [25] and relates the query complexity to the size of the sample. We start by providing some (mostly) textbook de nitions for self...
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BibTeX entry: (Update)
H. Buhrman and R. de Wolf. Complexity measures and decision tree complexity: A survey. Submitted. Available at http://www.cwi.nl/~rdewolf, 1999. http://citeseer.ist.psu.edu/buhrman00complexity.html More
@misc{ buwo02, author = "H. Buhrman and R. de Wolf",
title = "Complexity measures and decision tree complexity: A survey",
journal="Theoretical Computer Science",
volume="288",
pages="21-43",
year="2002",
url = "citeseer.ist.psu.edu/buhrman00complexity.html",
url = "citeseer.nj.nec.com/buhrman00complexity.html" }
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167 Quantum Computation and Quantum Information (context) - Nielsen, Chuang - 2000
134 Concrete Mathematics: A Foundation for Computer Science (context) - Graham, Knuth et al. - 1989
94 Upper and lower time bounds for parallel random access machi.. (context) - Cook, Dwork et al. - 1986
60 Generic oracles and oracle classes (context) - Blum, Impagliazzo - 1987
59 The influence of variables on Boolean functions (context) - Kahn, Kalai et al. - 1988
57 the degree of Boolean functions as real polynomials - Nisan, Szegedy - 1994
36 Complexity limitations on quantum computation - Fortnow, Rogers - 1999
32 On recognizing graph properties from adjacency matrices (context) - Rivest, Vuillemin - 1976
32 An oracle builder's toolkit - Fenner, Fortnow et al. - 1993
31 The polynomial method in circuit complexity - Beigel - 1993
29 Probabilistic Boolean decision trees and the complexity of e.. (context) - Saks, Wigderson - 1986
25 A topological approach to evasiveness (context) - Kahn, Saks et al. - 1984
21 Lower bounds for probabilistic linear decision trees (context) - Snir - 1985
21 lower bound on the randomized complexity of graph properties - Hajnal - 1991
19 Communication complexity lower bounds by polynomials - Buhrman, de Wolf - 1999
18 the degree of polynomials that approximate symmetric Boolean.. (context) - Paturi - 1992
16 Schwankung von Polynomen zwischen Gitterpunkten (context) - Ehlich, Zeller - 1964
16 Bounds for small-error and zero-error quantum algorithms - Buhrman, Cleve et al. - 1999
15 The quantum query complexity of approximating the median and.. - Nayak, Wu - 1999
11 Earlier version in STOC (context) - Nisan, decision et al. - 1991
11 A comparison of uniform approximations on an interval and a .. (context) - Rivlin, Cheney - 1966
11 Lower bounds on the complexity of graph properties (context) - King - 1988
11 bound on the time for parallel RAM's to compute non-degenera.. (context) - Simon, mega et al. - 1983
11 the Monte Carlo decision tree complexity of read-once formul.. (context) - Santha - 1991
10 The average sensitivity of bounded-depth circuits (context) - Boppana - 1997
10 robustness and the non-isomorphism of NP-complete sets (context) - Hartmanis, Hemachandra - 1987
9 Lecture notes on evasiveness of graph properties (context) - Lov'asz, Young - 1994
8 On read-once threshold formulae and their randomized decisio.. - Heiman, Newman et al. - 1993
7 Polynomials with two values (context) - Gathen, Roche - 1997
7 or why is it difficult to separate NP (context) - Tardos
7 A note on quantum black-box complexity of almost all Boolean.. (context) - Ambainis - 1999
6 deterministic decision tree complexity for read-once Boolean.. (context) - Heiman, Wigderson - 1991
6 How many functions can be distinguished with k quantum queri.. (context) - Farhi, Goldstone et al. - 1999
6 Space-time tradeoffs for graph properties - Dodis, Khanna - 1999
5 block sensitivity of Boolean functions (context) - Rubinstein - 1995
5 Earlier version in FOCS (context) - Nisan, Wigderson et al. - 1995
5 Lower bounds of quantum black-box complexity and degree of a.. (context) - Shi - 2000
3 Information Processing Letters (context) - Bernasconi, block et al. - 1996
3 Average-case quantum query complexity - Ambainis, de Wolf - 2000
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