-
1
-
-
0039681742
-
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
-
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
22
-
-
84878127882
-
Kolmogorov complexity
-
in: R.G. Downey, D.R. Hirschfeldt (Eds.); de Gruyter Series in Logic and its Applications; de Gruyter, Berlin
-
L. Fortnow, Kolmogorov complexity, in: R.G. Downey, D.R. Hirschfeldt (Eds.), Aspects of Complexity, Minicourses in Algorithmics, Complexity, and Computational Algebra, NZMRI Mathematics Summer Meeting, Kaikoura, New Zealand, January 7-15, 2000, de Gruyter Series in Logic and its Applications, Vol. 4, de Gruyter, Berlin, 2001, pp. 73-86.
-
(2001)
Aspects of Complexity, Minicourses in Algorithmics, Complexity, and Computational Algebra, NZMRI Mathematics Summer Meeting, Kaikoura, New Zealand, January 7-15, 2000
, vol.4
, pp. 73-86
-
-
Fortnow, L.1
-
23
-
-
0000189643
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
36
-
-
0003680739
-
-
Springer, New York
-
M. Li, P. Vitanyi, An Introduction to Kolmogorov Complexity and its Applications, 2nd Edition, Springer, New York, 1997.
-
(1997)
An Introduction to Kolmogorov Complexity and Its Applications, 2nd Edition
-
-
Li, M.1
Vitanyi, P.2
-
37
-
-
84974575141
-
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
-
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
-
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
-
Reals that compute little
-
to appear
-
A. Nies, Reals that compute little, to appear.
-
-
-
Nies, A.1
-
42
-
-
0001531051
-
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
-
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
-
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
-
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
-
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
-
Computability and differential geometry
-
to appear
-
R.I. Soare, Computability and differential geometry, to appear.
-
-
-
Soare, R.I.1
-
48
-
-
0011635934
-
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
-
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
-
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
-
-
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
-
52
-
-
77956964279
-
On random r.e. sets
-
in: A. Arruda, N. Da Costa, R. Chuaqui (Eds.); North-Holland, Amsterdam
-
R.M. Solovay, On random r.e. sets, in: A. Arruda, N. Da Costa, R. Chuaqui (Eds.), Non-Classical Logics, Model Theory, and Computability, Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, July 11-17, 1976, Studies in Logic and the Foundations of Mathematics, Vol. 89, North-Holland, Amsterdam, 1977, pp. 283-307.
-
(1977)
Non-Classical Logics, Model Theory, and Computability, Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, July 11-17, 1976, Studies in Logic and the Foundations of Mathematics
, vol.89
, pp. 283-307
-
-
Solovay, R.M.1
-
53
-
-
0842335187
-
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
-
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
-
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
-
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
-
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
|