We investigate the distribution of nonuniform complexities in uniform complexity classes. We prove that almost every problem decidable in exponential space has essentially maximum circuit-size and space-bounded Kolmogorov complexity almost everywhere. (The circuit-size lower bound actually exceeds, and thereby strengthens, the Shannon 2
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1083
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Introduction to Kolmogorov Complexity and Its Applications
– Li, Vitanyi
- 1993
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480
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How to construct random functions
– Goldreich, Goldwasser, et al.
- 1986
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466
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How to generate Cryptographically Strong Sequences of Pseudo-Random Bits
– Blum, Micali
- 1984
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415
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Theory and applications of trapdoor functions
– Yao
- 1982
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382
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Safeware, System Safety and Computers
– Leveson
- 1995
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304
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Three approaches to the quantitative definition of information
– Kolmogorov
- 1965
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240
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The definition of random sequences
– Martin-Löf
- 1966
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233
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A Formal Theory of Inductive Inference
– Solomonoff
- 1964
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219
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A theory of program size formally identical to information theory
– Chaitin
- 1975
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195
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Some connections between nonuniform and uniform complexity classes
– Karp, Lipton
- 1980
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186
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Algorithmic Information Theory
– Chaitin
- 1987
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161
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On the length of programs for computing finite binary sequences: Statistical considerations
– Chaitin
- 1969
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159
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Structural Complexity I
– Balc'azar, D'iaz, et al.
- 1988
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159
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Almost everywhere high nonuniform complexity
– Lutz
- 1992
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140
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Measure Theory
– Halmos
- 1974
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122
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Zuf"alligkeit und Wahrscheinlichkeit
– Schnorr
- 1971
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97
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The synthesis of two-terminal switching circuits
– Shannon
- 1949
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78
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Analyzing Software Requirements Errors in Safety-Critical, Embedded Systems
– Lutz
- 1993
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76
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The use of goals to surface requirements for evolving systems
– Antón, Potts
- 1998
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73
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On the notion of a random sequence
– Levin
- 1973
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69
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Quantitative Analysis of Faults and Failures in a Complex Software System
– Fenton, Ohlsson
- 2000
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64
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Requirements Monitoring in Dynamic Environments
– Feather, Fickas
- 1995
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62
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Category and measure in complexity classes
– Lutz
- 1990
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62
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A unified approach to the definition of random sequences
– Schnorr
- 1971
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58
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Process complexity and effective random tests
– Schnorr
- 1973
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57
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Relativized circuit complexity
– Wilson
- 1985
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55
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Circuit-size lower bounds and non-reducibility to sparse sets
– Kannan
- 1982
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48
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Generalized Kolmogorov complexity and the structure of feasible computations
– Hartmanis
- 1983
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45
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A guided tour of Cherno bounds
– Hagerup, Rub
- 1989
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40
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Random Sequences
– Lambalgen
- 1987
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35
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On the concept of random sequence
– Church
- 1940
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31
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Logical depth and physical complexity
– Bennett
- 1988
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30
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Resource-bounded measure
– Lutz
- 1998
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30
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The Change and Evolution of Requirements as a Challenge to the Practice of Software Engineering
– HARKER, EASON, et al.
- 1993
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30
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Every sequence is reducible to a random one
– Gács
- 1986
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29
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Π 0 1-classes and complete extensions of PA
– Measure
- 1985
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28
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Software maintenance and evolution: A roadmap
– Bennett, Rajlich
- 2000
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28
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Combinatorial foundations of information theory and the calculus of probabilities
– Kolmogorov
- 1983
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25
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Sets with small generalized Kolmogorov complexity
– Balc'azar, Book
- 1986
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24
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Incompleteness theorems for random reals
– Chaitin
- 1987
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23
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Mises, Grundlagen der Wahrscheinlichkeitsrechnung
– von
- 1919
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22
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Can an individual sequence of zeros and ones be random
– Shen´
- 1990
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21
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On the notion of infinite pseudorandom sequences
– Ko
- 1986
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21
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Klassifikation der Zufallsgesetze nach Komplexitat und Ordnung, Z. Wahrscheinlichkeitstheorie verw
– Schnorr
- 1970
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20
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On tables of random numbers
– Kolmogorov
- 1963
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19
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Some consequences of the existence of pseudorandom generators
– Allender
- 1989
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17
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Complexity oscillations in infinite binary sequences. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete
– Martin-Lof
- 1971
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16
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Kolmogorov complexity and degrees of tally sets
– Allender, Watanabe
- 1990
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16
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A complexity-theoretic approach to randomness
– Sipser
- 1983
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15
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Randomness and the density of hard problems
– Wilber
- 1983
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