{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T02:49:36Z","timestamp":1712458176171},"reference-count":20,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2004,10,1]],"date-time":"2004-10-01T00:00:00Z","timestamp":1096588800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2004,10]]},"abstract":"Abstract<\/jats:title>We examine the randomness and triviality of reals using notions arising from martingales and prefix\u2010free machines. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH & Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310121","type":"journal-article","created":{"date-parts":[[2004,10,4]],"date-time":"2004-10-04T16:01:01Z","timestamp":1096905661000},"page":"613-627","source":"Crossref","is-referenced-by-count":21,"title":["On Schnorr and computable randomness, martingales, and machines"],"prefix":"10.1002","volume":"50","author":[{"given":"Rod","family":"Downey","sequence":"first","affiliation":[]},{"given":"Evan","family":"Griffiths","sequence":"additional","affiliation":[]},{"given":"Geoffrey","family":"Laforte","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,10]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"K.Ambos\u2010Spies andA.Ku\u010dera Randomness in computability theory. In: Computability Theory: Current Trends and Open Problems (P. Cholak et al. eds.) Contemporary Mathematics 257 (2000) pp. 1\u201314 (American Math. Society Reading (MA) 2000).","DOI":"10.1090\/conm\/257\/04023"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"G. J.Chaitin Algorithmic Information Theory (Cambridge University Press Cambridge 1987).","DOI":"10.1017\/CBO9780511608858"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1082418542"},{"key":"e_1_2_1_5_2","unstructured":"R.Downey andD.Hirschfeldt Algorithmic Randomness and Complexity (Springer\u2010Verlag Berlin et al. to appear)."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2003.07.004"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"R.Downey D.Hirschfeldt andA.Nies Randomness computability and density. SIAM J. Comput.31 1169\u20131183 (2002). An extended abstract appeared in: Symposium for Theoretical Aspects of Computer Science STACS'01 January 2001 (A. Ferriera and H. Reichel eds.) Lecture Notes in Computer Science pp. 195\u2013201 (Springer\u2010Verlag Berlin et al. 2001).","DOI":"10.1007\/3-540-44693-1_17"},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","unstructured":"R. G.Downey D. R.Hirschfeldt A.Nies andF.Stephan Trivial reals. In: Electronic Notes in Theoretical Computer Science (ENTCS) 2002. The final version appears in Proceedings Asian Logic Conferences (R. G. Downey et al. eds.) pp. 103\u2013131 (World Scientific 2003).","DOI":"10.1142\/9789812705815_0005"},{"key":"e_1_2_1_9_2","unstructured":"R. G.Downey D. R.Hirschfeldt A.Nies andS.Terwijn Calibrating randomness. In preparation."},{"key":"e_1_2_1_10_2","first-page":"1413","article-title":"On the notion of a random sequence","volume":"14","author":"Levin L. A.","year":"1973","journal-title":"Soviet Math. Dokl."},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","unstructured":"M.Li andP.Vit\u00e1nyi An Introduction to Kolmogorov Complexity and its Applications (Springer\u2010Verlag Berlin et al. 1993).","DOI":"10.1007\/978-1-4757-3860-5"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539799357441"},{"key":"e_1_2_1_13_2","unstructured":"A.Nies Reals which compute little. To appear."},{"key":"e_1_2_1_14_2","unstructured":"A.Nies F.Stephan andS.Terwijn Randomness relativization and Turing degrees. In preparation."},{"key":"e_1_2_1_15_2","doi-asserted-by":"crossref","unstructured":"C.\u2010P.Schnorr Zuf\u00e4lligkeit und Wahrscheinlichkeit. Lecture Notes in Mathematics218(Springer\u2010Verlag Berlin\u2010 Heidelberg 1971).","DOI":"10.1007\/BFb0112458"},{"key":"e_1_2_1_16_2","doi-asserted-by":"crossref","unstructured":"R. I.Soare Recursively Enumerable Sets and Degrees. Perspectives in Mathematical Logic Omega Series (Springer\u2010 Verlag Berlin\u2010Heidelberg\u2010New York\u2010Tokyo 1987).","DOI":"10.1007\/978-3-662-02460-7"},{"key":"e_1_2_1_17_2","unstructured":"R.Solovay Draft of a paper (or series of papers) on Chaitin's work. Unpublished manuscript (IBM Thomas J. Watson Research Center New York May 1975 215 pp.)."},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00102-5"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.2307\/2695101"},{"key":"e_1_2_1_20_2","unstructured":"Y.Wang Randomness and Complexity. PhD Diss. University of Heidelberg 1996."},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1070\/RM1970v025n06ABEH001269"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310121","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310121","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T21:00:54Z","timestamp":1697662854000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310121"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10]]},"references-count":20,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2004,10]]}},"alternative-id":["10.1002\/malq.200310121"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310121","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,10]]}}}