메뉴 건너뛰기




Volumn 12, Issue 3, 2006, Pages 390-410

Randomness and computability: Open questions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33748541285     PISSN: 10798986     EISSN: None     Source Type: Journal    
DOI: 10.2178/bsl/1154698740     Document Type: Review
Times cited : (72)

References (55)
  • 1
    • 0039681742 scopus 로고    scopus 로고
    • Randomness in computability theory
    • (P. A. Cholak, S. Lempp, M. Lerman, and R. A. Shore, editors), Contemporary Mathematics, American Mathematical Society
    • K. AMBOS-SPIES and A. KUCERA, Randomness in computability theory, Computability Theory and its Applications (Boulder, CO, 1999) (P. A. Cholak, S. Lempp, M. Lerman, and R. A. Shore, editors), Contemporary Mathematics, vol. 257, American Mathematical Society, 2000, pp. 1-14.
    • (2000) Computability Theory and Its Applications (Boulder, CO, 1999) , vol.257 , pp. 1-14
    • Ambos-Spies, K.1    Kucera, A.2
  • 6
    • 0008780480 scopus 로고
    • Remarks on the structure of tt-degrees based on constructive measure theory
    • O. DEMUTH, Remarks on the structure of tt-degrees based on constructive measure theory, Commentationes Mathematicae Universitatis Carolinae, vol. 29 (1988), pp. 233-247.
    • (1988) Commentationes Mathematicae Universitatis Carolinae , vol.29 , pp. 233-247
    • Demuth, O.1
  • 15
    • 0022761997 scopus 로고
    • Every sequence is reducible to a random one
    • P. GÁCS, Every sequence is reducible to a random one, Information and Control, vol. 70 (1986), pp. 186-192.
    • (1986) Information and Control , vol.70 , pp. 186-192
    • Gács, P.1
  • 18
    • 0004290929 scopus 로고
    • Ph.D. Dissertation, Cornell University
    • S. KAUTZ, Degrees of random sets, Ph.D. Dissertation, Cornell University, 1991.
    • (1991) Degrees of Random Sets
    • Kautz, S.1
  • 20
    • 33745463530 scopus 로고    scopus 로고
    • Lowness for the class of Schnorr random reals
    • B. KJOS-HANSSEN, A. NIES, and F. STEPHAN, Lowness for the class of Schnorr random reals, SIAM Journal on Computing, vol. 35 (2006), no. 3, pp. 647-657.
    • (2006) SIAM Journal on Computing , vol.35 , Issue.3 , pp. 647-657
    • Kjos-Hanssen, B.1    Nies, A.2    Stephan, F.3
  • 21
    • 0000701330 scopus 로고
    • 0-classes and complete extensions of PA
    • (K. Ambos-Spies, G. H. Müller, and G. E. Sacks, editors), Lecture Notes in Mathematics, Springer
    • 0-classes and complete extensions of PA, Recursion Theory Week (Oberwolfach, 1984) (K. Ambos-Spies, G. H. Müller, and G. E. Sacks, editors), Lecture Notes in Mathematics, vol. 1141, Springer, 1985, pp. 245-259.
    • (1985) Recursion Theory Week (Oberwolfach, 1984) , vol.1141 , pp. 245-259
    • Kučera, A.1
  • 22
    • 84973252873 scopus 로고
    • An alternative, priority-free, solution to Post's problem
    • Lecture Notes in Computer Science, Springer
    • _, An alternative, priority-free, solution to Post's problem, Mathematical Foundations of Computer Science, 1986 (Bratislava, 1986), Lecture Notes in Computer Science, vol. 233, Springer, 1986, pp. 493-500.
    • (1986) Mathematical Foundations of Computer Science, 1986 (Bratislava, 1986) , vol.233 , pp. 493-500
  • 23
    • 0007506313 scopus 로고
    • On the role of 0′ in recursion theory
    • Studies in Logic and the Foundations of Mathematics, North-Holland
    • _, On the role of 0′ in recursion theory, Logic Colloquium '86 (Hull, 1986), Studies in Logic and the Foundations of Mathematics, vol. 124, North-Holland, 1988, pp. 133-141.
    • (1988) Logic Colloquium '86 (Hull, 1986) , vol.124 , pp. 133-141
  • 24
    • 38249002629 scopus 로고
    • On relative randomness
    • _, On relative randomness, Annals of Pure and Applied Logic, vol. 63 (1993), pp. 61-67.
    • (1993) Annals of Pure and Applied Logic , vol.63 , pp. 61-67
  • 26
    • 0003936721 scopus 로고
    • Perspectives in Mathematical Logic, SpringerVerlag
    • M. LERMAN, Degrees of unsolvability, Perspectives in Mathematical Logic, SpringerVerlag, 1983.
    • (1983) Degrees of Unsolvability
    • Lerman, M.1
  • 27
    • 84974575141 scopus 로고    scopus 로고
    • Gales and the constructive dimension of individual sequences
    • Lecture Notes in Computer Science, Springer
    • J. H. LUTZ, Gales and the constructive dimension of individual sequences. Automata, Languages and Programming (Geneva, 2000), Lecture Notes in Computer Science, vol. 1853, Springer, 2000, pp. 902-913.
    • (2000) Automata, Languages and Programming (Geneva, 2000) , vol.1853 , pp. 902-913
    • Lutz, J.H.1
  • 28
  • 29
    • 0037120704 scopus 로고    scopus 로고
    • A Kolmogorov complexity characterization of constructive Hausdorff dimension
    • E. MAYORDOMO, A Kolmogorov complexity characterization of constructive Hausdorff dimension, Information Processing Letters, vol. 84 (2002), no. 1, pp. 1-3.
    • (2002) Information Processing Letters , vol.84 , Issue.1 , pp. 1-3
    • Mayordomo, E.1
  • 30
    • 0043016187 scopus 로고    scopus 로고
    • The complexity of stochastic sequences
    • Aarhus, Denmark
    • W. MERKLE, The complexity of stochastic sequences, Conference on Computational Complexity 2003 (Aarhus, Denmark), vol. 64, 2003, pp. 230-235.
    • (2003) Conference on Computational Complexity 2003 , vol.64 , pp. 230-235
    • Merkle, W.1
  • 32
    • 4644309025 scopus 로고    scopus 로고
    • Every 2-random real is Kolmogorov random
    • J. S. MILLER, Every 2-random real is Kolmogorov random, The Journal of Symbolic Logic, vol. 69 (2004), pp. 907-913.
    • (2004) The Journal of Symbolic Logic , vol.69 , pp. 907-913
    • Miller, J.S.1
  • 37
    • 24644511669 scopus 로고    scopus 로고
    • Lowness properties and randomness
    • A. NIES, Lowness properties and randomness, Advances in Mathematics, vol. 197 (2005), pp. 274-305.
    • (2005) Advances in Mathematics , vol.197 , pp. 274-305
    • Nies, A.1
  • 38
    • 37249070657 scopus 로고    scopus 로고
    • Reals which compute little
    • (Z. Chatzidakis, P. Koepke, and W. Pohlers, editors), Lecture Notes in Logic, Association for Symbolic Logic
    • _, Reals which compute little, Logic Colloquium '02 (Z. Chatzidakis, P. Koepke, and W. Pohlers, editors), Lecture Notes in Logic, vol. 27, Association for Symbolic Logic, 2006, pp. 261-275.
    • (2006) Logic Colloquium '02 , vol.27 , pp. 261-275
  • 39
    • 24644497441 scopus 로고    scopus 로고
    • Oxford Logic Guides, Oxford University Press, to appear
    • _, Computability and randomness, Oxford Logic Guides, Oxford University Press, to appear.
    • Computability and Randomness
  • 41
  • 42
    • 35048824498 scopus 로고    scopus 로고
    • preprint
    • _, Low for random sets: the story, preprint; available at http://www.cs. auckland.ac.nz/nies/papers/.
    • Low for Random Sets: the Story
  • 44
    • 20444494956 scopus 로고    scopus 로고
    • Randomness, relativization and Turing degrees
    • A. NIES, F. STEPHAN, and S. A. TERWIJN, Randomness, relativization and Turing degrees, The Journal of Symbolic Logic, vol. 70 (2005), no. 2, pp. 515-535.
    • (2005) The Journal of Symbolic Logic , vol.70 , Issue.2 , pp. 515-535
    • Nies, A.1    Stephan, F.2    Terwijn, S.A.3
  • 45
    • 24144450113 scopus 로고    scopus 로고
    • Doctoral dissertation, Universität Heidelberg
    • J. REIMANN, Computability and fractal dimension, Doctoral dissertation, Universität Heidelberg, 2004, Available at http://math.uni-heidelberg.de/ logic/reimazin/ publications/phdthesis.pdf.
    • (2004) Computability and Fractal Dimension
    • Reimann, J.1
  • 46
    • 26444528871 scopus 로고
    • Coding of combinatorial sources and Hausdorff dimension
    • B. Y. RYABKO, Coding of combinatorial sources and Hausdorff dimension, Doklady Akademii Nauk SSSR, vol. 277 (1984), no. 5, pp. 1066-1070.
    • (1984) Doklady Akademii Nauk SSSR , vol.277 , Issue.5 , pp. 1066-1070
    • Ryabko, B.Y.1
  • 47
    • 0004107182 scopus 로고
    • Perspectives in Mathematical Logic, SpringerVerlag
    • G. SACKS, Higher recursion theory, Perspectives in Mathematical Logic, SpringerVerlag, 1990.
    • (1990) Higher Recursion Theory
    • Sacks, G.1
  • 50
    • 10444249657 scopus 로고    scopus 로고
    • Constructive dimension equals Kolmogorov complexity
    • L. STAIGER, Constructive dimension equals Kolmogorov complexity, Information Processing Letters, vol. 93 (2005), no. 3, pp. 149-153.
    • (2005) Information Processing Letters , vol.93 , Issue.3 , pp. 149-153
    • Staiger, L.1
  • 51
    • 33748551199 scopus 로고    scopus 로고
    • Martin-Löf random sets and PA-complete sets
    • (Z. Chatzidakis, P. Koepke, and W. Pohlers, editors), Lecture Notes in Logic, Association for Symbolic Logic
    • F. STEPHAN, Martin-Löf random sets and PA-complete sets. Logic Colloquium '02 (Z. Chatzidakis, P. Koepke, and W. Pohlers, editors), Lecture Notes in Logic, vol. 27, Association for Symbolic Logic, 2006, pp. 342-348.
    • (2006) Logic Colloquium '02 , vol.27 , pp. 342-348
    • Stephan, F.1
  • 53
    • 0035633478 scopus 로고    scopus 로고
    • Algorithmic randomness and lowness
    • S. A. TERWIJN and D. ZAMBELLA, Algorithmic randomness and lowness, The Journal of Symbolic Logic, vol. 66 (2001), no. 3, pp. 1199-1205.
    • (2001) The Journal of Symbolic Logic , vol.66 , Issue.3 , pp. 1199-1205
    • Terwijn, S.A.1    Zambella, D.2
  • 54
    • 0040988824 scopus 로고
    • The axiomatization of randomness
    • M. VAN LAMBALGEN, The axiomatization of randomness. The Journal of Symbolic Logic, vol. 55 (1990), no. 3, pp. 1143-1167.
    • (1990) The Journal of Symbolic Logic , vol.55 , Issue.3 , pp. 1143-1167
    • Van Lambalgen, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.