메뉴 건너뛰기




Volumn 37, Issue 3, 2007, Pages 671-705

Effective strong dimension in algorithmic information and computational complexity

Author keywords

Computational complexity; Effective dimension; Hausdorff dimension; Kolmogorov complexity; Martin L f randomness; Packing dimension

Indexed keywords

(2+1) DIMENSIONS; (ALGORITHMIC) COMPLEXITY; BASIC PROPERTIES; BOOLEAN CIRCUITS; CAMBRIDGE; COMPLEXITY CONSTRAINTS; EFFECTIVE DIMENSIONS; FINITE STATES; FLORENCE , ITALY; FRACTAL GEOMETRY; GALE CHARACTERIZATION; GENERAL (CO); HAUSDORFF; HAUSDORFF DIMENSIONS; KOLMOGOROV COMPLEXITY (KC); PACKING DIMENSION; POLYNOMIAL TIME DEGREES; POLYNOMIAL-TIME; SIZE COMPLEXITY;

EID: 34948824745     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539703446912     Document Type: Article
Times cited : (99)

References (49)
  • 2
    • 0031070091 scopus 로고    scopus 로고
    • Resource bounded randomness and weakly complete problems
    • K. AMBOS-SPIES, S. A. TERWIJN, AND X. ZHENG, Resource bounded randomness and weakly complete problems, Theoret. Comput. Sci., 172 (1997), pp. 195-207.
    • (1997) Theoret. Comput. Sci , vol.172 , pp. 195-207
    • AMBOS-SPIES, K.1    TERWIJN, S.A.2    ZHENG, X.3
  • 4
    • 0342733652 scopus 로고    scopus 로고
    • Equivalence of measures of complexity classes
    • J. M. BREUTZMANN AND J. H. LUTZ, Equivalence of measures of complexity classes, SIAM J. Comput., 29 (1999), pp. 302-326.
    • (1999) SIAM J. Comput , vol.29 , pp. 302-326
    • BREUTZMANN, J.M.1    LUTZ, J.H.2
  • 5
    • 0028712369 scopus 로고
    • On Hausdorff and topological dimensions of the Kolmogorov complexity of the real line
    • J. CAI AND J. HARTMANIS, On Hausdorff and topological dimensions of the Kolmogorov complexity of the real line, J. Comput. Systems Sci., 49 (1994), pp. 605-619.
    • (1994) J. Comput. Systems Sci , vol.49 , pp. 605-619
    • CAI, J.1    HARTMANIS, J.2
  • 6
    • 0016532771 scopus 로고
    • A theory of program size formally identical to information theory
    • G. J. CHAITIN, A theory of program size formally identical to information theory, J. ACM, 22 (1975), pp. 329-340.
    • (1975) J. ACM , vol.22 , pp. 329-340
    • CHAITIN, G.J.1
  • 10
    • 46449133755 scopus 로고    scopus 로고
    • S. A. FENNER, Gales and Supergales are Equivalent for Defining Constructive Hausdorff Dimension, Technical Report cs.CC/0208044, Computing Research Repository, Cornell University, Ithaca, NY, 2002.
    • S. A. FENNER, Gales and Supergales are Equivalent for Defining Constructive Hausdorff Dimension, Technical Report cs.CC/0208044, Computing Research Repository, Cornell University, Ithaca, NY, 2002.
  • 11
  • 12
    • 34250950477 scopus 로고
    • Dimension und äußeres Maß
    • F. HAUSDORFF, Dimension und äußeres Maß, Math. Ann., 79 (1919), pp. 157-179.
    • (1919) Math. Ann , vol.79 , pp. 157-179
    • HAUSDORFF, F.1
  • 13
    • 0037163961 scopus 로고    scopus 로고
    • MAX3SAT is exponentially hard to approximate if NP has positive dimension
    • J. M. HITCHCOCK, MAX3SAT is exponentially hard to approximate if NP has positive dimension, Theoret. Comput. Sci., 289 (2002), pp. 861-869.
    • (2002) Theoret. Comput. Sci , vol.289 , pp. 861-869
    • HITCHCOCK, J.M.1
  • 14
    • 0037811185 scopus 로고    scopus 로고
    • Fractal dimension and logarithmic loss unpredictability
    • J. M. HITCHCOCK, Fractal dimension and logarithmic loss unpredictability, Theoret. Comput. Sci., 304 (2003), pp. 431-441.
    • (2003) Theoret. Comput. Sci , vol.304 , pp. 431-441
    • HITCHCOCK, J.M.1
  • 15
    • 0037447594 scopus 로고    scopus 로고
    • Gales suffice for constructive dimension
    • J. M. HITCHCOCK, Gales suffice for constructive dimension, Inform. Process. Lett., 86 (2003), pp. 9-12.
    • (2003) Inform. Process. Lett , vol.86 , pp. 9-12
    • HITCHCOCK, J.M.1
  • 16
    • 23844521264 scopus 로고    scopus 로고
    • Correspondence principles for effective dimensions
    • J. M. HITCHCOCK, Correspondence principles for effective dimensions, Theory Comput. Systems, 38 (2005), pp. 559-571.
    • (2005) Theory Comput. Systems , vol.38 , pp. 559-571
    • HITCHCOCK, J.M.1
  • 17
    • 0000616816 scopus 로고
    • On the equivalence of infinite product measures
    • S. KAKUTANI, On the equivalence of infinite product measures, Ann. Math., 49 (1948), pp. 214-224.
    • (1948) Ann. Math , vol.49 , pp. 214-224
    • KAKUTANI, S.1
  • 20
    • 0026851355 scopus 로고
    • Almost everywhere high nonuniform complexity
    • J. H. LUTZ, Almost everywhere high nonuniform complexity, J. Comput. System Sci., 44 (1992), pp. 220-258.
    • (1992) J. Comput. System Sci , vol.44 , pp. 220-258
    • LUTZ, J.H.1
  • 22
    • 0033718506 scopus 로고    scopus 로고
    • Dimension in complexity classes
    • Florence, Italy, IEEE Computer Society Press, Piscataway, NJ
    • J. LUTZ, Dimension in complexity classes, in Proceedings of the 15th IEEE Conference on Computational Complexity, Florence, Italy, 2000, IEEE Computer Society Press, Piscataway, NJ, 2000, pp. 158-169.
    • (2000) Proceedings of the 15th IEEE Conference on Computational Complexity , pp. 158-169
    • LUTZ, J.1
  • 23
    • 0345227319 scopus 로고    scopus 로고
    • Dimension in complexity classes
    • J. H. LUTZ, Dimension in complexity classes, SIAM J. Comput., 32 (2003), pp. 1236-1259.
    • (2003) SIAM J. Comput , vol.32 , pp. 1236-1259
    • LUTZ, J.H.1
  • 24
    • 0344118726 scopus 로고    scopus 로고
    • The dimensions of individual strings and sequences
    • J. H. LUTZ, The dimensions of individual strings and sequences, Inform. Comput., 187 (2003), pp. 49-79.
    • (2003) Inform. Comput , vol.187 , pp. 49-79
    • LUTZ, J.H.1
  • 25
    • 18344371384 scopus 로고
    • The definition of random sequences
    • P. MARTIN-LÖF, The definition of random sequences, Information and Control, 9 (1966), pp. 602-619.
    • (1966) Information and Control , vol.9 , pp. 602-619
    • MARTIN-LÖF, P.1
  • 26
    • 21444447771 scopus 로고    scopus 로고
    • Measure and dimension functions: Measurability and densities
    • P. MATTILA AND R. MAULDIN, Measure and dimension functions: Measurability and densities, Math. Proc. Cambridge Philos. Soc., 121 (1997), pp. 81-100.
    • (1997) Math. Proc. Cambridge Philos. Soc , vol.121 , pp. 81-100
    • MATTILA, P.1    MAULDIN, R.2
  • 27
    • 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), pp. 1-3.
    • (2002) Inform. Process. Lett , vol.84 , pp. 1-3
    • MAYORDOMO, E.1
  • 29
    • 0004492226 scopus 로고
    • Coding of combinatorial sources and Hausdorff dimension
    • B. YA, RYABKO, Coding of combinatorial sources and Hausdorff dimension, Soviet Math. Dokl., 30 (1984), pp. 219-222.
    • (1984) Soviet Math. Dokl , vol.30 , pp. 219-222
    • YA, B.1    RYABKO2
  • 30
    • 0022741249 scopus 로고
    • Noiseless coding of combinatorial sources
    • B. YA, RYABKO, Noiseless coding of combinatorial sources, Probl. Inform. Transm., 22 (1986), pp. 170-179.
    • (1986) Probl. Inform. Transm , vol.22 , pp. 170-179
    • YA, B.1    RYABKO2
  • 31
    • 0004018518 scopus 로고
    • Algorithmic approach to the prediction problem
    • B. YA, RYABKO, Algorithmic approach to the prediction problem, Probl. Inform. Transm., 29 (1993), pp. 186-193.
    • (1993) Probl. Inform. Transm , vol.29 , pp. 186-193
    • YA, B.1    RYABKO2
  • 32
    • 0000797906 scopus 로고
    • The complexity and effectiveness of prediction problems
    • B. YA, RYABKO, The complexity and effectiveness of prediction problems, J. Complexity, 10 (1994), pp. 281-295.
    • (1994) J. Complexity , vol.10 , pp. 281-295
    • YA, B.1    RYABKO2
  • 33
    • 0000583779 scopus 로고
    • A unified approach to the definition of random sequences
    • C. P. SCHNORR, A unified approach to the definition of random sequences, Math. Systems Theory, 5 (1971), pp. 246-258.
    • (1971) Math. Systems Theory , vol.5 , pp. 246-258
    • SCHNORR, C.P.1
  • 34
    • 0002411710 scopus 로고
    • Zufälligkeit und Wahrscheinlichkeit
    • Springer-Verlag, New York
    • C. P. SCHNORR, Zufälligkeit und Wahrscheinlichkeit, Lecture Notes in Math. 218, Springer-Verlag, New York, 1971.
    • (1971) Lecture Notes in Math , vol.218
    • SCHNORR, C.P.1
  • 35
    • 0015902552 scopus 로고
    • Process complexity and effective random tests
    • C. P. SCHNORR, Process complexity and effective random tests, J. Comput. System Sci., 7 (1973), pp. 376-388.
    • (1973) J. Comput. System Sci , vol.7 , pp. 376-388
    • SCHNORR, C.P.1
  • 36
    • 46449122384 scopus 로고    scopus 로고
    • C. P. SCHNORR, A survey of the theory of random sequences, in Basic Problems in Methodology and Linguistics, R. E. Butts and J. Hintikka, eds., D. Reidel, Boston, 1977, pp. 193-211.
    • C. P. SCHNORR, A survey of the theory of random sequences, in Basic Problems in Methodology and Linguistics, R. E. Butts and J. Hintikka, eds., D. Reidel, Boston, 1977, pp. 193-211.
  • 37
    • 84940644968 scopus 로고    scopus 로고
    • C. E. SHANNON, A mathematical theory of communication, Bell System Tech. J., 27 (1948), pp. 379-423, 623-656.
    • C. E. SHANNON, A mathematical theory of communication, Bell System Tech. J., 27 (1948), pp. 379-423, 623-656.
  • 38
    • 38249002230 scopus 로고
    • Kolmogorov complexity and Hausdorff dimension
    • L. STAIGER, Kolmogorov complexity and Hausdorff dimension, Inform. Comput., 103 (1993), pp. 159-194.
    • (1993) Inform. Comput , vol.103 , pp. 159-194
    • STAIGER, L.1
  • 39
    • 0038856793 scopus 로고    scopus 로고
    • A tight upper bound on Kolmogorov complexity and uniformly optimal prediction
    • L. STAIGER, A tight upper bound on Kolmogorov complexity and uniformly optimal prediction, Theory Comput. Syst., 31 (1998), pp. 215-229.
    • (1998) Theory Comput. Syst , vol.31 , pp. 215-229
    • STAIGER, L.1
  • 40
    • 46449122701 scopus 로고    scopus 로고
    • L. STAIGER, How much can you win when your adversary is handicapped?, in Numbers, Information and Complexity, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000, pp. 403-412.
    • L. STAIGER, How much can you win when your adversary is handicapped?, in Numbers, Information and Complexity, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000, pp. 403-412.
  • 41
    • 0000144097 scopus 로고
    • Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
    • D. SULLIVAN, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math., 153 (1984), pp. 259-277.
    • (1984) Acta Math , vol.153 , pp. 259-277
    • SULLIVAN, D.1
  • 42
    • 10444239935 scopus 로고    scopus 로고
    • A generalization of Chaitin's halting probability Ω and halting self-similar sets
    • K. TADAKI, A generalization of Chaitin's halting probability Ω and halting self-similar sets, Hokkaido Math. J., 31 (2002), pp. 219-253.
    • (2002) Hokkaido Math. J , vol.31 , pp. 219-253
    • TADAKI, K.1
  • 43
    • 84971877468 scopus 로고
    • Two definitions of fractional dimension
    • C. TRICOT, Two definitions of fractional dimension, Math. Proc. Cambridge Philos. Soc., 91 (1982), pp. 57-74.
    • (1982) Math. Proc. Cambridge Philos. Soc , vol.91 , pp. 57-74
    • TRICOT, C.1
  • 44
    • 38049164974 scopus 로고
    • Ph.D. thesis, Department of Mathematics, University of Amsterdam, Amsterdam
    • M. VAN LAMBALGEN, Random Sequences, Ph.D. thesis, Department of Mathematics, University of Amsterdam, Amsterdam, 1987.
    • (1987) Random Sequences
    • VAN LAMBALGEN, M.1
  • 45
    • 0000651254 scopus 로고
    • Von Mises' definition of random sequences reconsidered
    • M. VAN LAMBALGEN, Von Mises' definition of random sequences reconsidered, J. Symbolic Logic, 52 (1987), pp. 725 755.
    • (1987) J. Symbolic Logic , vol.52 , pp. 725-755
    • VAN LAMBALGEN, M.1
  • 47
    • 0000727615 scopus 로고
    • On a randomness criterion
    • V. G. VOVK, On a randomness criterion, Soviet Math. Dokl., 35 (1987), pp. 656-660.
    • (1987) Soviet Math. Dokl , vol.35 , pp. 656-660
    • VOVK, V.G.1
  • 48
    • 0017996424 scopus 로고
    • Coding theorems for individual sequences
    • J. ZIV, Coding theorems for individual sequences, IEEE Trans. Inform. Theory, 24 (1978), pp. 405-412.
    • (1978) IEEE Trans. Inform. Theory , vol.24 , pp. 405-412
    • ZIV, J.1
  • 49
    • 0018019231 scopus 로고
    • Compression of individual sequences via variable rate coding
    • J. ZIV AND A. LEMPEL, Compression of individual sequences via variable rate coding, IEEE Trans. Inform. Theory, 24 (1978), pp. 530-536.
    • (1978) IEEE Trans. Inform. Theory , vol.24 , pp. 530-536
    • ZIV, J.1    LEMPEL, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.