{"id":"https://openalex.org/W1756323827","doi":"https://doi.org/10.1134/s0032946009010074","title":"Algorithmic randomness and splitting of supermartingales","display_name":"Algorithmic randomness and splitting of supermartingales","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W1756323827","doi":"https://doi.org/10.1134/s0032946009010074","mag":"1756323827"},"language":"en","primary_location":{"id":"doi:10.1134/s0032946009010074","is_oa":true,"landing_page_url":"https://doi.org/10.1134/s0032946009010074","pdf_url":"https://link.springer.com/content/pdf/10.1134/S0032946009010074.pdf","source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1134/S0032946009010074.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083035277","display_name":"An. A. Muchnik","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"An. A. Muchnik","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083035277"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.06003541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"45","issue":"1","first_page":"54","last_page":"64"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9610000252723694,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.8785827159881592},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7880818843841553},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36363673210144043},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3495407700538635},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34759312868118286},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1422530710697174}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.8785827159881592},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7880818843841553},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36363673210144043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3495407700538635},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34759312868118286},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1422530710697174}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0032946009010074","is_oa":true,"landing_page_url":"https://doi.org/10.1134/s0032946009010074","pdf_url":"https://link.springer.com/content/pdf/10.1134/S0032946009010074.pdf","source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1134/s0032946009010074","is_oa":true,"landing_page_url":"https://doi.org/10.1134/s0032946009010074","pdf_url":"https://link.springer.com/content/pdf/10.1134/S0032946009010074.pdf","source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1756323827.pdf","grobid_xml":"https://content.openalex.org/works/W1756323827.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1639327804","https://openalex.org/W1979604519","https://openalex.org/W1979734360"],"related_works":["https://openalex.org/W2351859806","https://openalex.org/W2354664641","https://openalex.org/W4239376463","https://openalex.org/W1996810073","https://openalex.org/W2089811522","https://openalex.org/W2111700426","https://openalex.org/W1993700123","https://openalex.org/W2525105177","https://openalex.org/W2388813193","https://openalex.org/W2092244978"],"abstract_inverted_index":{"Randomness":[0],"in":[1,9],"the":[2,47],"sense":[3],"of":[4,11,27],"Martin-L\u00f6f":[5],"can":[6],"be":[7,22],"defined":[8],"terms":[10],"lower":[12],"semicomputable":[13],"supermartingales.":[14],"We":[15],"show":[16],"that":[17,29],"such":[18],"a":[19,25],"supermartingale":[20],"cannot":[21],"replaced":[23],"by":[24],"pair":[26],"supermartingales":[28],"bet":[30],"only":[31],"on":[32,39],"even":[33],"bits":[34,41],"(the":[35,42],"first":[36],"one)":[37,44],"and":[38],"odd":[40],"second":[43],"knowing":[45],"all":[46],"preceding":[48],"bits.":[49]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}