Some remarks on pseudorandom sequences

Reinhard Winkler

Mathematica Slovaca (1993)

  • Volume: 43, Issue: 4, page 493-512
  • ISSN: 0139-9918

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Winkler, Reinhard. "Some remarks on pseudorandom sequences." Mathematica Slovaca 43.4 (1993): 493-512. <http://eudml.org/doc/31810>.

@article{Winkler1993,
author = {Winkler, Reinhard},
journal = {Mathematica Slovaca},
keywords = {permutable sets; terminal sets; pseudorandom sequence; discrepancy; test of randomness; sets of acceptance; invariant sets; Baire properties},
language = {eng},
number = {4},
pages = {493-512},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Some remarks on pseudorandom sequences},
url = {http://eudml.org/doc/31810},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Winkler, Reinhard
TI - Some remarks on pseudorandom sequences
JO - Mathematica Slovaca
PY - 1993
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 43
IS - 4
SP - 493
EP - 512
LA - eng
KW - permutable sets; terminal sets; pseudorandom sequence; discrepancy; test of randomness; sets of acceptance; invariant sets; Baire properties
UR - http://eudml.org/doc/31810
ER -

References

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  1. CHAITIN G. J., Algorithmic Information Theory, Cambridge University Press, 1987, 1988, 1990. (1987) Zbl1013.00525MR0917482
  2. CHAITIN G. J., Information, Randomness and Incompleteness - Papers on Algorithmic Information Theory, World Scientific, Singapore, 1987, 1990. (1987) Zbl1013.00525MR1153671
  3. CHAITIN G. J., Incompleteness theorems for random reals, Adv. in Appl. Math. 8 (1987), 119-146. (1987) Zbl0649.03046MR0886921
  4. CHURCH A., On the concept of a random sequence, Bull. Amer. Math. Soc. 46 (1940), 130-135. (1940) Zbl0022.36904MR0000911
  5. DÖRGE K., Zu der von R. v. Mises gegebenen Begrtindung der Wahrscheinlichkeitstheorie, Math. Z. 32 (1930), 232-258. (1930) MR1545164
  6. DRMOTA M., TICHY R. F., WINKLER R., Completely uniformly distributed sequences of matrices, In: Number-Theoretic Analysis. Lecture Notes in Math. 1452, Springer, Berlin-Heidelberg-New York, 1990, pp. 43-57. (1990) Zbl0717.11030MR1084637
  7. DRMOTA M., WINKLER R., s(N)-uniform distribution modulo 1, J. Number Theory, (To appear). Zbl0826.11034MR1316817
  8. FELLER W., An Introduction to Probability Theory and its Applications, John Wiley and Sons Inc., New York-London-Sydney-Toronto, 1966. (1966) Zbl0138.10207MR0210154
  9. FELLER W., Über die Existenz sogenannter Kollektive, Fund. Math. 32 (1939), 87-96. (1939) 
  10. FLAJOLET P., KIRSCHENHOFER P., TICHY R. F., Discrepancy of Sequences in Infinite Strings, Colloq. Math. Soc. Janos Bolyai, North-Holland, Amsterdam-New York, 1986. (1986) 
  11. FLAJOLET P., KIRSCHENHOFER P., TICHY R. F., Deviations from uniformity in random strings, Probab. Theory Related Fields 80 (1988), 139-150. (1988) Zbl0638.68058MR0970475
  12. GOLDSTERN M., An application of Shoenfield's absoluteness theorem to the theory of uniform distribution, Monatsh. Math., (To appear). Zbl0811.11053MR1253684
  13. GOLDSTERN M., Two more remarks on pseudorandom sequences, (Preprint). 
  14. GRABNER P., Block distribution in random strings, Ann. Inst. Fourier (Grenoble), (To appear). Zbl0778.60023MR1220283
  15. GRILL K., A note on randomness, Statist. Probab. Letters 14 (1992), 229-233. (1992) Zbl0809.60038MR1173623
  16. HLAWKA E., Theorie der Gleichverteilung, Bibl. Inst., Mannheim-Wien-Zürich, 1979. (1979) Zbl0406.10001MR0542905
  17. KIRSCHENHOFER P., TICHY R. F., Some distribution properties of 0-1 -sequences, Manuscripta Math. 54 (1985), 205-219. (1985) Zbl0599.10045MR0808689
  18. KNUTH D. E., The Art of Computer Programming. Vol. II, Addison-Wesley, Reading Mass., 1981. (1981) MR0633878
  19. KOLMOGOROFF A. N., Grundbegriffe der Wahrscheinlichkeitsrechnung, Ergeb. Math. Grenzgeb. (2), Springer, Berlin-New York, 1933. (1933) Zbl0007.21601MR0494348
  20. KOLMOGOROFF A. N., Drei Zugänge zur Definition des Begriffs "Informationsgehalt", (Russian), Problemy Peredachi Informatsii 1 (1965), 3-11. (1965) 
  21. KOLMOGOROFF A. N., On tables of random numbers, Sankhya Ser. A 25 (1963), 369-376. (1963) MR0178484
  22. KUIPERS L., NIEDERREITER H., Uniform Distribution of Sequences, Wiley, New York, 1974. (1974) Zbl0281.10001MR0419394
  23. van LAMBALGEN M., Von Mises' definition of random sequences reconsidered, J. Symbolic Logic 52 (1987), 725-755. (1987) Zbl0628.60001MR0902987
  24. LEVIN L. A., On the notion of a random sequence, Soviet Math. Dokl. 14 (1973), 1414-1416. (1973) Zbl0312.94006
  25. LEVINE M. B., On the uniform distribution of the sequence {αλx}, (Russian), Mat. Sb. 98 (1975), 207-222, (Translation: Math. USSR-Sb. 27 (1975), 183-197). (1975) MR0406947
  26. LEVINE M. B., On the completely uniform distribution of fractional parts of the exponentional function, (Russian, English Summary), Trudy Sem. Im. Petrovsk. 7 (1981), 245-256. (1981) MR0656508
  27. LEVITAN, YU. L., SHUKHMAN B. V., SOBOL I. M., TURCHANINOV V. I., Quasirandom Sequence Generators, Keldysh Inst., of Appl. Math., Russian Acad, of Sciences, 1992. (1992) MR1211861
  28. MARTIN-LÖF P., The definition of random sequences, Inform. Control 9 (1966), 602-619. (1966) MR0223179
  29. MARTIN-LÖF P., On the notion of randomness, In: Intuitionism Proof Theory Proc. Summer Conf. Buffalo N.Y. 1968, 1970, pp. 73-78. (1968) MR0275483
  30. von MISES R., Grundlagen der Wahrscheinlichkeitstheorie, Math. Z. 5 (1919), 52-99. (1919) MR1544374
  31. von MISES R., Wahrscheinlichkeit, Statistik und Wahrheit, Springer, Wien, 1951. (1951) Zbl0043.13002
  32. von MISES R., Mathematical Theory of Probability and Statistics, Acad. Press, New York-London, 1964. (1964) Zbl0132.12303MR0178486
  33. NIEDERREITER H., Quasi-Monte Carlo methods and pseudorandom numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041. (1978) MR0508447
  34. NIEDERREITER H., Pseudozufallszahlen und die Theorie der Gleichverteilung, Sitzungsber. Österreich. Akad. Wiss. Math.-Natur. Kl. Abt. II 195 (1986), 109-138. (195) MR0881335
  35. NIEDERREITER H., Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. (1987) Zbl0626.10045MR0918037
  36. NIEDERREITER H., Pseudorandom numbers generated from shift register sequences, In: Number-Theoretic Analysis. Lecture Notes in Math. 1452 (E. Hlawka, R. F. Tichy, eds.), Springer, Berlin-Heidelberg-New York, 1990, pp. 165-177. (1990) Zbl0718.11034MR1084645
  37. NIEDERREITER H., Random Number Generation and Quasi-Monte Carlo Methods, Society for industrial and applied mathematics, Philadelphia, Pennsylvania, 1992. (1992) Zbl0761.65002MR1172997
  38. NIEDERREITER H., TICHY R. F., Solution of a problem of Knuth on complete uniform distribution of sequences, Mathematika 23 (1985), 26-32. (1985) Zbl0582.10036MR0817103
  39. POPPER K., Logik der Forschung, Achte, weitere verbesserte und vermehrte Auflage, J. C. B. Mohr (Paul Siebeck), Tübingen, 1984. (1984) MR1290323
  40. SCHNORR C. P., Zufälligkeit und Wahrscheinlichkeit, Eine algorithmische Begründung der Wahrscheinlichkeitstheorie, Lecture Notes in Math. 218, Springer, Berlin-Heidelberg-New York, 1971. (1971) Zbl0232.60001MR0414225
  41. SCHNORR C. P., Process complexity and effective random tests, J. Comput. System Sci. 7 (1973), 376-388. (1973) Zbl0273.68036MR0325366
  42. SOBOL I. M., Quasi-Monte Carlo methods, Progress in Nuclear Energy 24 (1990), 55-61. (1990) MR1102293
  43. SOBOL I. M., Die Monte-Carlo-Methode, Deutscher Verlag der Wissenschaften, Berlin, 1991. (1991) Zbl0719.65001MR1188646
  44. SVOZIL K., The mathematical foundations of physical randomness and indeterminisness, In: Jahrb. Kurt-Gödel-Ges., Wien, 1988, pp. 53-85. (1988) MR1023328
  45. TAUSWORTHE R. C., Random numbers generated by linear recurrence modulo two, Math. Comp. 19 (1965), 201-209. (1965) Zbl0137.34804MR0184406
  46. TEZUKA S., On the discrepancy of GFSR pseudorandom numbers, J. Assoc. Comput. Math. 34 (1987), 939-949. (1987) Zbl0633.65005MR0913848
  47. TEZUKA S., On optimal GFSR pseudorandom number generators, Math. Comp. 50 (1988), 531-533. (1988) Zbl0644.65004MR0929550
  48. TICHY R. F., Ein metrischer Satz über vollständig gleichverteilte Folgen, Acta Arith. 48 (1987), 197-207. (1987) Zbl0574.10049MR0895440
  49. TICHY R. F., Zur Analyse und Anwendung von Zufallszahlen, In: Jahrb. Kurt-Gödel-Ges., Wien, 1990, pp. 109-116. (1990) MR1143713
  50. VILLE J., Etude critique de la notion de collectif, Gauthier-Villars, Paris, 1939. (1939) Zbl0021.14601
  51. WALD A., Sur la notion de collectif dans le calcul des probabilites, C. R. Acad. Sci. Paris 202 (1936), 180-183. (1936) Zbl0013.12304
  52. WALD A., Die Widerspruchsfreiheit des Kollektivbegriffs in der Wahrscheinlichkeitsrechnung, Ergebnisse eines math. Koll. 8 (1937), 38-72. (1937) 
  53. WINKLER R., Some constructive examples in uniform distribution on finite sets and normal numbers, Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 126 (1989), 1-8. (1989) Zbl0671.10046MR1086459

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