{"id":"https://openalex.org/W2015908112","doi":"https://doi.org/10.1137/s0097539792232070","title":"Matrix Transformation Is Complete for the Average Case","display_name":"Matrix Transformation Is Complete for the Average Case","publication_year":1995,"publication_date":"1995-02-01","ids":{"openalex":"https://openalex.org/W2015908112","doi":"https://doi.org/10.1137/s0097539792232070","mag":"2015908112"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539792232070","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792232070","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043571692","display_name":"Andreas Blass","orcid":"https://orcid.org/0000-0001-7445-2980"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andreas Blass","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065430432","display_name":"Yuri Gurevich","orcid":"https://orcid.org/0000-0001-7808-9293"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuri Gurevich","raw_affiliation_strings":["(University of Michigan)"],"affiliations":[{"raw_affiliation_string":"(University of Michigan)","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043571692"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.2987,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.95346342,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"24","issue":"1","first_page":"3","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9976999759674072,"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/T11567","display_name":"semigroups and automata theory","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unimodular-matrix","display_name":"Unimodular matrix","score":0.8604788780212402},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7794011831283569},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7541537284851074},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.6815220713615417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5328056812286377},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5314140915870667},{"id":"https://openalex.org/keywords/identity-matrix","display_name":"Identity matrix","score":0.47806671261787415},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.441936194896698},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4411925971508026},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42221498489379883},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4157503843307495}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.8604788780212402},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7794011831283569},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7541537284851074},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.6815220713615417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5328056812286377},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5314140915870667},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.47806671261787415},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.441936194896698},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4411925971508026},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42221498489379883},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4157503843307495},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539792232070","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792232070","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.47.5287","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.5287","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.research.microsoft.com/~gurevich/Opera/97.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.61.2787","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.2787","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/~gurevich/Opera/97.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W189633613","https://openalex.org/W204707887","https://openalex.org/W1435322393","https://openalex.org/W1537344488","https://openalex.org/W1545962847","https://openalex.org/W1993375595","https://openalex.org/W2000138878","https://openalex.org/W2011039300","https://openalex.org/W2012473793","https://openalex.org/W2019084979","https://openalex.org/W2021320809","https://openalex.org/W2028907144","https://openalex.org/W2074876220","https://openalex.org/W2100008268","https://openalex.org/W2107993699","https://openalex.org/W2110836275","https://openalex.org/W2152708687","https://openalex.org/W2167954650","https://openalex.org/W2186921161","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W3175367423","https://openalex.org/W4234361933","https://openalex.org/W4238118247","https://openalex.org/W4255062480"],"related_works":["https://openalex.org/W2011745869","https://openalex.org/W2088028898","https://openalex.org/W1974942973","https://openalex.org/W2950905816","https://openalex.org/W211627054","https://openalex.org/W1608437562","https://openalex.org/W1971653407","https://openalex.org/W2963754540","https://openalex.org/W2617189160","https://openalex.org/W2141735856"],"abstract_inverted_index":{"In":[0,28],"the":[1,18,29,42,48,75,130],"theory":[2,30,52],"of":[3,31,44,94,99,102,117,124],"worst":[4],"case":[5,33,36,50,64,77],"complexity,":[6,34],"NP":[7,20,45],"completeness":[8,37],"is":[9,22,38,53,83,87,114],"used":[10],"to":[11,40,129],"establish":[12],"that,":[13],"for":[14,74],"all":[15],"practical":[16],"purposes,":[17],"given":[19],"problem":[21,72,86],"not":[23],"decidable":[24],"in":[25],"polynomial":[26],"time.":[27],"average":[32,35,49,63,76],"supposed":[39],"play":[41],"role":[43],"completeness.":[46],"However,":[47],"reduction":[51],"still":[54],"at":[55],"an":[56],"early":[57],"stage,":[58],"and":[59,106],"only":[60],"a":[61,79,90,96,107,115],"few":[62],"complete":[65,73],"problems":[66],"are":[67],"known.":[68],"The":[69,85],"first":[70],"algebraic":[71],"under":[78],"natural":[80,108],"probability":[81],"distribution":[82],"presented.":[84],"this:":[88],"Given":[89],"unimodular":[91,104],"matrix":[92],"X":[93,128],"integers,":[95],"set":[97],"S":[98,125],"linear":[100],"transformations":[101],"such":[103],"matrices":[105],"number":[109],"n,":[110],"decide":[111],"if":[112],"there":[113],"product":[116],"$\\leq":[118],"n$":[119],"(not":[120],"necessarily":[121],"different)":[122],"members":[123],"that":[126],"takes":[127],"identity":[131],"matrix.":[132]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}