Some remarks on pseudorandom sequences
Mathematica Slovaca (1993)
- Volume: 43, Issue: 4, page 493-512
- ISSN: 0139-9918
Access Full Article
topHow to cite
topWinkler, 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
top- CHAITIN G. J., Algorithmic Information Theory, Cambridge University Press, 1987, 1988, 1990. (1987) Zbl1013.00525MR0917482
- CHAITIN G. J., Information, Randomness and Incompleteness - Papers on Algorithmic Information Theory, World Scientific, Singapore, 1987, 1990. (1987) Zbl1013.00525MR1153671
- CHAITIN G. J., Incompleteness theorems for random reals, Adv. in Appl. Math. 8 (1987), 119-146. (1987) Zbl0649.03046MR0886921
- CHURCH A., On the concept of a random sequence, Bull. Amer. Math. Soc. 46 (1940), 130-135. (1940) Zbl0022.36904MR0000911
- DÖRGE K., Zu der von R. v. Mises gegebenen Begrtindung der Wahrscheinlichkeitstheorie, Math. Z. 32 (1930), 232-258. (1930) MR1545164
- 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
- DRMOTA M., WINKLER R., s(N)-uniform distribution modulo 1, J. Number Theory, (To appear). Zbl0826.11034MR1316817
- FELLER W., An Introduction to Probability Theory and its Applications, John Wiley and Sons Inc., New York-London-Sydney-Toronto, 1966. (1966) Zbl0138.10207MR0210154
- FELLER W., Über die Existenz sogenannter Kollektive, Fund. Math. 32 (1939), 87-96. (1939)
- 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)
- FLAJOLET P., KIRSCHENHOFER P., TICHY R. F., Deviations from uniformity in random strings, Probab. Theory Related Fields 80 (1988), 139-150. (1988) Zbl0638.68058MR0970475
- GOLDSTERN M., An application of Shoenfield's absoluteness theorem to the theory of uniform distribution, Monatsh. Math., (To appear). Zbl0811.11053MR1253684
- GOLDSTERN M., Two more remarks on pseudorandom sequences, (Preprint).
- GRABNER P., Block distribution in random strings, Ann. Inst. Fourier (Grenoble), (To appear). Zbl0778.60023MR1220283
- GRILL K., A note on randomness, Statist. Probab. Letters 14 (1992), 229-233. (1992) Zbl0809.60038MR1173623
- HLAWKA E., Theorie der Gleichverteilung, Bibl. Inst., Mannheim-Wien-Zürich, 1979. (1979) Zbl0406.10001MR0542905
- KIRSCHENHOFER P., TICHY R. F., Some distribution properties of 0-1 -sequences, Manuscripta Math. 54 (1985), 205-219. (1985) Zbl0599.10045MR0808689
- KNUTH D. E., The Art of Computer Programming. Vol. II, Addison-Wesley, Reading Mass., 1981. (1981) MR0633878
- KOLMOGOROFF A. N., Grundbegriffe der Wahrscheinlichkeitsrechnung, Ergeb. Math. Grenzgeb. (2), Springer, Berlin-New York, 1933. (1933) Zbl0007.21601MR0494348
- KOLMOGOROFF A. N., Drei Zugänge zur Definition des Begriffs "Informationsgehalt", (Russian), Problemy Peredachi Informatsii 1 (1965), 3-11. (1965)
- KOLMOGOROFF A. N., On tables of random numbers, Sankhya Ser. A 25 (1963), 369-376. (1963) MR0178484
- KUIPERS L., NIEDERREITER H., Uniform Distribution of Sequences, Wiley, New York, 1974. (1974) Zbl0281.10001MR0419394
- van LAMBALGEN M., Von Mises' definition of random sequences reconsidered, J. Symbolic Logic 52 (1987), 725-755. (1987) Zbl0628.60001MR0902987
- LEVIN L. A., On the notion of a random sequence, Soviet Math. Dokl. 14 (1973), 1414-1416. (1973) Zbl0312.94006
- 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
- 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
- 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
- MARTIN-LÖF P., The definition of random sequences, Inform. Control 9 (1966), 602-619. (1966) MR0223179
- 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
- von MISES R., Grundlagen der Wahrscheinlichkeitstheorie, Math. Z. 5 (1919), 52-99. (1919) MR1544374
- von MISES R., Wahrscheinlichkeit, Statistik und Wahrheit, Springer, Wien, 1951. (1951) Zbl0043.13002
- von MISES R., Mathematical Theory of Probability and Statistics, Acad. Press, New York-London, 1964. (1964) Zbl0132.12303MR0178486
- NIEDERREITER H., Quasi-Monte Carlo methods and pseudorandom numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041. (1978) MR0508447
- NIEDERREITER H., Pseudozufallszahlen und die Theorie der Gleichverteilung, Sitzungsber. Österreich. Akad. Wiss. Math.-Natur. Kl. Abt. II 195 (1986), 109-138. (195) MR0881335
- NIEDERREITER H., Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. (1987) Zbl0626.10045MR0918037
- 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
- NIEDERREITER H., Random Number Generation and Quasi-Monte Carlo Methods, Society for industrial and applied mathematics, Philadelphia, Pennsylvania, 1992. (1992) Zbl0761.65002MR1172997
- 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
- POPPER K., Logik der Forschung, Achte, weitere verbesserte und vermehrte Auflage, J. C. B. Mohr (Paul Siebeck), Tübingen, 1984. (1984) MR1290323
- 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
- SCHNORR C. P., Process complexity and effective random tests, J. Comput. System Sci. 7 (1973), 376-388. (1973) Zbl0273.68036MR0325366
- SOBOL I. M., Quasi-Monte Carlo methods, Progress in Nuclear Energy 24 (1990), 55-61. (1990) MR1102293
- SOBOL I. M., Die Monte-Carlo-Methode, Deutscher Verlag der Wissenschaften, Berlin, 1991. (1991) Zbl0719.65001MR1188646
- SVOZIL K., The mathematical foundations of physical randomness and indeterminisness, In: Jahrb. Kurt-Gödel-Ges., Wien, 1988, pp. 53-85. (1988) MR1023328
- TAUSWORTHE R. C., Random numbers generated by linear recurrence modulo two, Math. Comp. 19 (1965), 201-209. (1965) Zbl0137.34804MR0184406
- TEZUKA S., On the discrepancy of GFSR pseudorandom numbers, J. Assoc. Comput. Math. 34 (1987), 939-949. (1987) Zbl0633.65005MR0913848
- TEZUKA S., On optimal GFSR pseudorandom number generators, Math. Comp. 50 (1988), 531-533. (1988) Zbl0644.65004MR0929550
- TICHY R. F., Ein metrischer Satz über vollständig gleichverteilte Folgen, Acta Arith. 48 (1987), 197-207. (1987) Zbl0574.10049MR0895440
- TICHY R. F., Zur Analyse und Anwendung von Zufallszahlen, In: Jahrb. Kurt-Gödel-Ges., Wien, 1990, pp. 109-116. (1990) MR1143713
- VILLE J., Etude critique de la notion de collectif, Gauthier-Villars, Paris, 1939. (1939) Zbl0021.14601
- WALD A., Sur la notion de collectif dans le calcul des probabilites, C. R. Acad. Sci. Paris 202 (1936), 180-183. (1936) Zbl0013.12304
- WALD A., Die Widerspruchsfreiheit des Kollektivbegriffs in der Wahrscheinlichkeitsrechnung, Ergebnisse eines math. Koll. 8 (1937), 38-72. (1937)
- 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
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.