메뉴 건너뛰기




Volumn 68, Issue 1, 2004, Pages 96-114

Randomness and reducibility

Author keywords

Algorithmic information theory; Computably enumerable reals; Kolmogorov complexity; Relative randomness; Solovay reducibility

Indexed keywords

ALGORITHMS; COMPUTABILITY AND DECIDABILITY; INFORMATION THEORY; RANDOM PROCESSES;

EID: 0842300595     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcss.2003.07.004     Document Type: Article
Times cited : (47)

References (57)
  • 1
    • 0039681742 scopus 로고    scopus 로고
    • Randomness in computability theory
    • in: P.A. Cholak, S. Lempp, M. Lerman, R.A. Shore (Eds.); Boulder, CO
    • K. Ambos-Spies, A. Kučera, Randomness in computability theory, in: P.A. Cholak, S. Lempp, M. Lerman, R.A. Shore (Eds.), Computability Theory and Its Applications, Boulder, CO, 1999
    • (1999) Computability Theory and Its Applications
    • Ambos-Spies, K.1    Kučera, A.2
  • 2
    • 0004125136 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, RI
    • K. Ambos-Spies, A. Kučera, Contemporary Mathematics, Vol. 257, American Mathematical Society, Providence, RI, 2000, pp. 1-14.
    • (2000) Contemporary Mathematics , vol.257 , pp. 1-14
    • Ambos-Spies, K.1    Kučera, A.2
  • 4
    • 0000738839 scopus 로고
    • Complexity of programs to determine whether natural numbers not greater than n belong to a recursively enumerable set
    • J. Barzdins, Complexity of programs to determine whether natural numbers not greater than n belong to a recursively enumerable set, Soviet Math. Dokl. 9 (1968) 1251-1254.
    • (1968) Soviet Math. Dokl. , vol.9 , pp. 1251-1254
    • Barzdins, J.1
  • 5
    • 0037185197 scopus 로고    scopus 로고
    • A characterization of c.e. random reals
    • C.S. Calude, A characterization of c.e. random reals, Theoret. Comput. Sci. 271 (2002) 3-14.
    • (2002) Theoret. Comput. Sci. , vol.271 , pp. 3-14
    • Calude, C.S.1
  • 6
    • 0003686516 scopus 로고
    • Information and randomness, an algorithmic perspective
    • Springer, Berlin
    • C.S. Calude, Information and Randomness, an Algorithmic Perspective, Monographs in Theoretical Computer Science, Springer, Berlin, 1994.
    • (1994) Monographs in Theoretical Computer Science
    • Calude, C.S.1
  • 7
    • 0006893032 scopus 로고    scopus 로고
    • Program-size complexity of initial segments and domination reducibility
    • in: J. Karhumäki, H. Maurer, G. P̌un, G. Rozenberg (Eds.); Springer, Berlin
    • C.S. Calude, R.J. Coles, Program-size complexity of initial segments and domination reducibility, in: J. Karhumäki, H. Maurer, G. P̌un, G. Rozenberg (Eds.), Jewels are Forever, Springer, Berlin, 1999, pp. 225-237.
    • (1999) Jewels are Forever , pp. 225-237
    • Calude, C.S.1    Coles, R.J.2
  • 8
    • 0003236129 scopus 로고    scopus 로고
    • Degree-theoretic aspects of computably enumerable reals
    • in: S.B. Cooper, J.K. Truss (Eds.), Models and Computability, Leeds, 1997; Cambridge University Press, Cambridge
    • C.S. Calude, R.J. Coles, P.H. Hertling, B. Khoussainov, Degree-theoretic aspects of computably enumerable reals, in: S.B. Cooper, J.K. Truss (Eds.), Models and Computability, Leeds, 1997, London Mathematical Society Lecture Note Series, Vol 259, Cambridge University Press, Cambridge, 1999, pp. 23-39.
    • (1999) London Mathematical Society Lecture Note Series , vol.259 , pp. 23-39
    • Calude, C.S.1    Coles, R.J.2    Hertling, P.H.3    Khoussainov, B.4
  • 9
    • 78649893518 scopus 로고    scopus 로고
    • Recursively enumerable reals and Chaitin Ω numbers
    • Centre for Discrete Mathematics and Theoretical Computer Science Research Report Series 59, University of Auckland, October 1997 (extended abstract in STACS 98, Lecture Notes in Computer Science, Vol. 1373, Springer, Berlin, 1998, pp. 596-606.)
    • C.S. Calude, P.H. Hertling, B. Khoussainov, Y. Wang, Recursively enumerable reals and Chaitin Ω numbers, Centre for Discrete Mathematics and Theoretical Computer Science Research Report Series 59, University of Auckland, October 1997 (extended abstract in STACS 98, Lecture Notes in Computer Science, Vol. 1373, Springer, Berlin, 1998, pp. 596-606.)
    • (1997)
    • Calude, C.S.1    Hertling, P.H.2    Khoussainov, B.3    Wang, Y.4
  • 10
    • 33751505024 scopus 로고    scopus 로고
    • Chaitin Ω numbers and strong reducibilities
    • C.S. Calude, A. Nies, Chaitin Ω numbers and strong reducibilities, J. Univ. Comput. Sci. 3 (1998) 1162-1166.
    • (1998) J. Univ. Comput. Sci. , vol.3 , pp. 1162-1166
    • Calude, C.S.1    Nies, A.2
  • 11
    • 0000702396 scopus 로고
    • A pseudofundamental sequence that is not equivalent to a monotone one
    • (in Russian with English summary)
    • G.S. Ceǐtin, A pseudofundamental sequence that is not equivalent to a monotone one, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 20 (1971) 263-271 290 (in Russian with English summary).
    • (1971) Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol.20
    • Ceǐtin, G.S.1
  • 12
    • 0016532771 scopus 로고
    • A theory of program size formally identical to information theory
    • (reprinted in [14])
    • G.J. Chaitin, A theory of program size formally identical to information theory, J. Assoc. Comput. Mach. 22 (1975) 329-340 (reprinted in [14]).
    • (1975) J. Assoc. Comput. Mach. , vol.22 , pp. 329-340
    • Chaitin, G.J.1
  • 13
    • 0000303535 scopus 로고
    • Algorithmic information theory
    • (reprinted in [14])
    • G.J. Chaitin, Algorithmic information theory, IBM J. Res. Develop. 21 (1977) 350-359 496 (reprinted in [14]).
    • (1977) IBM J. Res. Develop. , vol.21
    • Chaitin, G.J.1
  • 14
    • 0000761947 scopus 로고
    • Incompleteness theorems for random reals
    • (reprinted in [14])
    • G.J. Chaitin, Incompleteness theorems for random reals, Adv. in Appl. Math. 8 (1987) 119-146 (reprinted in [14]).
    • (1987) Adv. in Appl. Math. , vol.8 , pp. 119-146
    • Chaitin, G.J.1
  • 15
    • 0003781307 scopus 로고
    • Information, randomness & incompleteness
    • 2nd Edition, World Scientific, River Edge, NJ
    • G.J. Chaitin, Information, Randomness & Incompleteness, Series in Computer Science, Vol. 8, 2nd Edition, World Scientific, River Edge, NJ, 1990.
    • (1990) Series in Computer Science , vol.8
    • Chaitin, G.J.1
  • 16
    • 24244446377 scopus 로고    scopus 로고
    • Applications of computability theory to prime models and differential geometry
    • Ph.D. Dissertation, University of Chicago
    • B.F. Csima, Applications of computability theory to prime models and differential geometry, Ph.D. Dissertation, University of Chicago, 2003.
    • (2003)
    • Csima, B.F.1
  • 17
    • 0003519950 scopus 로고    scopus 로고
    • Some computability-theoretical aspects of reals and randomness
    • to appear in a volume of the Lecture Notes in Logic series published by the Association for Symbolic Logic
    • R. Downey, Some computability-theoretical aspects of reals and randomness, to appear in a volume of the Lecture Notes in Logic series published by the Association for Symbolic Logic.
    • Downey, R.1
  • 19
    • 0036520623 scopus 로고    scopus 로고
    • Randomness, computability, and density
    • (extended abstract, in: A. Ferreira, H. Reichel (Eds.), STACS 2001 Proceedings, Lecture Notes in Computer Science, Vol. 2010, Springer, Berlin, 2001, pp. 195-205.)
    • R. Downey, D.R. Hirschfeldt, A. Nies, Randomness, computability, and density, SIAM J. Comput. 21 (2002) 1169-1183 (extended abstract, in: A. Ferreira, H. Reichel (Eds.), STACS 2001 Proceedings, Lecture Notes in Computer Science, Vol. 2010, Springer, Berlin, 2001, pp. 195-205.)
    • (2002) SIAM J. Comput. , vol.31 , pp. 1169-1183
    • Downey, R.1    Hirschfeldt, D.R.2    Nies, A.3
  • 20
    • 3543080744 scopus 로고    scopus 로고
    • Trivial reals
    • to appear in: R. Downey, D. Decheng, T.S. Ping, Q.Y. Hui, M. Yasugi (Eds.); to be published by World Scientific (extended abstract in Electronic Notes in Theoretical Computer Science, Vol. 66)
    • R. Downey, D.R. Hirschfeldt, A. Nies, F. Stephan, Trivial reals, to appear in: R. Downey, D. Decheng, T.S. Ping, Q.Y. Hui, M. Yasugi (Eds.), Proceedings of the 7th and 8th Asian Logic Conferences, to be published by World Scientific (extended abstract in Electronic Notes in Theoretical Computer Science, Vol. 66).
    • Proceedings of the 7th and 8th Asian Logic Conferences
    • Downey, R.1    Hirschfeldt, D.R.2    Nies, A.3    Stephan, F.4
  • 21
    • 0037189782 scopus 로고    scopus 로고
    • Presentations of computably enumerable reals
    • R. Downey, G. LaForte, Presentations of computably enumerable reals, Theoret. Comput. Sci. 284 (2002) 539-555.
    • (2002) Theoret. Comput. Sci. , vol.284 , pp. 539-555
    • Downey, R.1    LaForte, G.2
  • 23
    • 0000189643 scopus 로고
    • On the symmetry of algorithmic information
    • P. Gács, On the symmetry of algorithmic information, Soviet Math. Dokl. 15 (1974) 1477-1480.
    • (1974) Soviet Math. Dokl. , vol.15 , pp. 1477-1480
    • Gács, P.1
  • 24
    • 0002452077 scopus 로고    scopus 로고
    • Relatively recursive reals and real functions
    • C. Ho, Relatively recursive reals and real functions, Theoret. Comput. Sci. 210 (1999) 99-120.
    • (1999) Theoret. Comput. Sci. , vol.210 , pp. 99-120
    • Ho, C.1
  • 25
    • 0001799236 scopus 로고
    • On the definition of some complexity classes of real numbers
    • K.-I. Ko, On the definition of some complexity classes of real numbers, Math. Systems Theory 16 (1983) 95-100.
    • (1983) Math. Systems Theory , vol.16 , pp. 95-100
    • Ko, K.-I.1
  • 26
    • 0022957598 scopus 로고
    • On the continued fraction representation of computable real numbers
    • K.-I. Ko, On the continued fraction representation of computable real numbers, Theoret. Comput. Sci. 47 (1986) 299-313.
    • (1986) Theoret. Comput. Sci. , vol.47 , pp. 299-313
    • Ko, K.-I.1
  • 27
    • 0001902056 scopus 로고
    • Three approaches to the definition of information
    • (in Russian)
    • A.N. Kolmogorov, Three approaches to the definition of information, Problems Inf. Transmission 1 (1965) 3-11 (in Russian).
    • (1965) Problems Inf. Transmission , vol.1 , pp. 3-11
    • Kolmogorov, A.N.1
  • 28
    • 84888288499 scopus 로고
    • Three approaches to the quantitative definition of information
    • A.N. Kolmogorov, Three approaches to the quantitative definition of information, Internat. J. Comput. Math. 2 (1968) 157-168.
    • (1968) Internat. J. Comput. Math. , vol.2 , pp. 157-168
    • Kolmogorov, A.N.1
  • 29
    • 0842270496 scopus 로고
    • Three approaches to the definition of the concept of the 'amount of information'
    • A.N. Kolmogorov, Three approaches to the definition of the concept of the 'amount of information', Select. Transl. Math. Stat. Probab. 7 (1968) 293-302.
    • (1968) Select. Transl. Math. Stat. Probab. , vol.7 , pp. 293-302
    • Kolmogorov, A.N.1
  • 30
    • 0036214633 scopus 로고    scopus 로고
    • Randomness and recursive enumerability
    • A. Kučera, T. Slaman, Randomness and recursive enumerability, SIAM J. Comput. 31 (2001) 199-211.
    • (2001) SIAM J. Comput. , vol.31 , pp. 199-211
    • Kučera, A.1    Slaman, T.2
  • 31
    • 0009975816 scopus 로고    scopus 로고
    • Kolmogorov complexity and instance complexity of recursively enumerable sets
    • M. Kummer, Kolmogorov complexity and instance complexity of recursively enumerable sets, SIAM J. Comput. 25 (1996) 1123-1143.
    • (1996) SIAM J. Comput. , vol.25 , pp. 1123-1143
    • Kummer, M.1
  • 32
    • 0001917363 scopus 로고
    • Recursive real numbers
    • A.H. Lachlan, Recursive real numbers, J. Symbolic Logic 28 (1963) 1-16.
    • (1963) J. Symbolic Logic , vol.28 , pp. 1-16
    • Lachlan, A.H.1
  • 33
    • 0000508181 scopus 로고
    • On the notion of a random sequence
    • L.A. Levin, On the notion of a random sequence, Soviet Math. Dokl. 14 (1973) 1413-1416.
    • (1973) Soviet Math. Dokl. , vol.14 , pp. 1413-1416
    • Levin, L.A.1
  • 34
    • 33750865993 scopus 로고
    • Laws of information conservation (non-growth) and aspects of the foundations of probability theory
    • (in Russian)
    • L.A. Levin, Laws of information conservation (non-growth) and aspects of the foundations of probability theory, Problemy Peredaci Informatsci 10 (1974) 30-35 (in Russian).
    • (1974) Problemy Peredaci Informatsci , vol.10 , pp. 30-35
    • Levin, L.A.1
  • 35
    • 0001041068 scopus 로고
    • The various measures of the complexity of finite objects (an axiomatic description)
    • L.A. Levin, The various measures of the complexity of finite objects (an axiomatic description), Soviet Math. Dokl. 17 (1976) 522-526.
    • (1976) Soviet Math. Dokl. , vol.17 , pp. 522-526
    • Levin, L.A.1
  • 37
    • 84974575141 scopus 로고    scopus 로고
    • The dimensions of individual strings and sequences
    • to appear (preliminary version: Gales and the constructive dimension of individual sequences, in: U. Montanari (Ed.), Automata, Languages, and Programming, 27th International Colloquium, ICALP 2000, Lecture Notes in Computer Science, Vol. 1853, Springer, Berlin, 2000, pp. 902-913.)
    • J. Lutz, The dimensions of individual strings and sequences, Inf. Comput., to appear (preliminary version: Gales and the constructive dimension of individual sequences, in: U. Montanari (Ed.), Automata, Languages, and Programming, 27th International Colloquium, ICALP 2000, Lecture Notes in Computer Science, Vol. 1853, Springer, Berlin, 2000, pp. 902-913.)
    • Inf. Comput
    • Lutz, J.1
  • 38
    • 18344371384 scopus 로고
    • The definition of random sequences
    • P. Martin-Löf, The definition of random sequences, Inform. and Control 9 (1966) 602-619.
    • (1966) Inform. and Control , vol.9 , pp. 602-619
    • Martin-Löf, P.1
  • 39
    • 0037120704 scopus 로고    scopus 로고
    • A Kolmogorov complexity characterization of constructive Hausdorff dimension
    • E. Mayordomo, A Kolmogorov complexity characterization of constructive Hausdorff dimension, Inform Process. Lett. 84 (2002) 1-3.
    • (2002) Inform Process. Lett. , vol.84 , pp. 1-3
    • Mayordomo, E.1
  • 41
    • 85030913735 scopus 로고    scopus 로고
    • Reals that compute little
    • to appear
    • A. Nies, Reals that compute little, to appear.
    • Nies, A.1
  • 42
    • 0001531051 scopus 로고
    • Recursive real numbers
    • H. Rice, Recursive real numbers, Proc. Amer. Math. Soc. 5 (1954) 784-791.
    • (1954) Proc. Amer. Math. Soc. , vol.5 , pp. 784-791
    • Rice, H.1
  • 43
    • 0015902552 scopus 로고
    • Process complexity and effective random tests
    • C.-P. Schnorr, Process complexity and effective random tests, J. Comput. System Sci. 7 (1973) 376-388.
    • (1973) J. Comput. System Sci. , vol.7 , pp. 376-388
    • Schnorr, C.-P.1
  • 44
    • 84972500791 scopus 로고
    • Cohesive sets and recursively enumerable Dedekind cuts
    • R.I. Soare, Cohesive sets and recursively enumerable Dedekind cuts, Pacific J. Math. 31 (1969) 215-231.
    • (1969) Pacific J. Math. , vol.31 , pp. 215-231
    • Soare, R.I.1
  • 45
    • 0000645113 scopus 로고
    • Recursion theory and Dedekind cuts
    • R.I. Soare, Recursion theory and Dedekind cuts, Trans. Amer. Math. Soc. 140 (1969) 271-294.
    • (1969) Trans. Amer. Math. Soc. , vol.140 , pp. 271-294
    • Soare, R.I.1
  • 46
    • 0003412510 scopus 로고
    • Recursively enumerable sets and degrees
    • Springer, Berlin
    • R.I. Soare, Recursively Enumerable Sets and Degrees, Springer, Berlin, 1987.
    • (1987)
    • Soare, R.I.1
  • 47
    • 85030905391 scopus 로고    scopus 로고
    • Computability and differential geometry
    • to appear
    • R.I. Soare, Computability and differential geometry, to appear.
    • Soare, R.I.1
  • 48
    • 0011635934 scopus 로고
    • A preliminary report on a general theory of inductive inference
    • Tech. Report ZTB-138, Zator Company, Cambridge, MA, November
    • R.J. Solomonoff, A preliminary report on a general theory of inductive inference, Tech. Report ZTB-138, Zator Company, Cambridge, MA, November, 1960.
    • (1960)
    • Solomonoff, R.J.1
  • 49
    • 4544279425 scopus 로고
    • A formal theory of inductive inference I
    • R.J. Solomonoff, A formal theory of inductive inference I, Inform. and Control 7 (1964) 1-22.
    • (1964) Inform. and Control , vol.7 , pp. 1-22
    • Solomonoff, R.J.1
  • 50
    • 50549204079 scopus 로고
    • A formal theory of inductive inference II
    • R.J. Solomonoff, A formal theory of inductive inference II, Inform. and Control 7 (1964) 224-254.
    • (1964) Inform. and Control , vol.7 , pp. 224-254
    • Solomonoff, R.J.1
  • 51
    • 85030900886 scopus 로고    scopus 로고
    • Draft of a paper (or series of papers) on Chaitin's work...done for the most part during the peroid of Sept.-Dec. 1974, May 1975, IBM Thomas J. Watson Research Center, Yorktown Heights, NY; unpublished
    • R.M. Solovay, Draft of a paper (or series of papers) on Chaitin's work...done for the most part during the peroid of Sept.-Dec. 1974, May 1975, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 215p., unpublished.
    • Solovay, R.M.1
  • 53
    • 0842335187 scopus 로고    scopus 로고
    • Constructive dimension equals Kolmogorov complexity
    • Research Report CDMTCS 210, Auckland University
    • L. Staiger, Constructive dimension equals Kolmogorov complexity, Research Report CDMTCS 210, Auckland University, 2003.
    • (2003)
    • Staiger, L.1
  • 54
    • 0011565585 scopus 로고
    • Random sequences
    • Ph.D. Dissertation, University of Amsterdam
    • M. van Lambalgen, Random sequences, Ph.D. Dissertation, University of Amsterdam, 1987.
    • (1987)
    • Van Lambalgen, M.1
  • 55
    • 35048876388 scopus 로고    scopus 로고
    • There is no sw-complete c.e. real
    • to appear
    • L. Yu, D. Ding, There is no sw-complete c.e. real, J. Symbolic Logic, to appear.
    • J. Symbolic Logic
    • Yu, L.1    Ding, D.2
  • 56
    • 0039556334 scopus 로고
    • On sequences with simple initial segments
    • Technical Report, Institute for Language, Logic and Information, University of Amsterdam
    • D. Zambella, On sequences with simple initial segments, Technical Report, Institute for Language, Logic and Information, University of Amsterdam, 1990.
    • (1990)
    • Zambella, D.1
  • 57
    • 77951203397 scopus 로고
    • The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms
    • A.K. Zvonkin, L.A. Levin, The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms, Russ. Math. Surv. 25 (1970) 83-124.
    • (1970) Russ. Math. Surv. , vol.25 , pp. 83-124
    • Zvonkin, A.K.1    Levin, L.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.