{"id":"https://openalex.org/W1934943886","doi":"https://doi.org/10.26421/qic14.15-16-3","title":"Strong equivalence of reversible circuits is coNP-complete","display_name":"Strong equivalence of reversible circuits is coNP-complete","publication_year":2014,"publication_date":"2014-11-01","ids":{"openalex":"https://openalex.org/W1934943886","doi":"https://doi.org/10.26421/qic14.15-16-3","mag":"1934943886"},"language":"en","primary_location":{"id":"doi:10.26421/qic14.15-16-3","is_oa":false,"landing_page_url":"https://doi.org/10.26421/qic14.15-16-3","pdf_url":null,"source":{"id":"https://openalex.org/S41034432","display_name":"Quantum Information and Computation","issn_l":"1533-7146","issn":["1533-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322612","host_organization_name":"Rinton Press","host_organization_lineage":["https://openalex.org/P4310322612"],"host_organization_lineage_names":["Rinton Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information and Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1307.0836","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045082038","display_name":"Stephen P. Jordan","orcid":"https://orcid.org/0000-0003-1035-1827"},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"funder","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stephen P. Jordan","raw_affiliation_strings":["Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD#TAB#"],"affiliations":[{"raw_affiliation_string":"Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD#TAB#","institution_ids":["https://openalex.org/I1321296531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045082038"],"corresponding_institution_ids":["https://openalex.org/I1321296531"],"apc_list":null,"apc_paid":null,"fwci":0.8478,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80086343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"15&16","first_page":"1302","last_page":"1307"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9954000115394592,"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/toffoli-gate","display_name":"Toffoli gate","score":0.9393510818481445},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.7422018647193909},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6577945947647095},{"id":"https://openalex.org/keywords/weak-equivalence","display_name":"Weak equivalence","score":0.6462768912315369},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5834425687789917},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5521796345710754},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5232366919517517},{"id":"https://openalex.org/keywords/logical-equivalence","display_name":"Logical equivalence","score":0.47025954723358154},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3200346827507019},{"id":"https://openalex.org/keywords/quantum-gate","display_name":"Quantum gate","score":0.251758337020874},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14154666662216187},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11310416460037231},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.107442706823349},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.07749819755554199}],"concepts":[{"id":"https://openalex.org/C142465778","wikidata":"https://www.wikidata.org/wiki/Q2502619","display_name":"Toffoli gate","level":5,"score":0.9393510818481445},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7422018647193909},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6577945947647095},{"id":"https://openalex.org/C2776863286","wikidata":"https://www.wikidata.org/wiki/Q17104639","display_name":"Weak equivalence","level":3,"score":0.6462768912315369},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5834425687789917},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5521796345710754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5232366919517517},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.47025954723358154},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3200346827507019},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.251758337020874},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14154666662216187},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11310416460037231},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.107442706823349},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.07749819755554199},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.26421/qic14.15-16-3","is_oa":false,"landing_page_url":"https://doi.org/10.26421/qic14.15-16-3","pdf_url":null,"source":{"id":"https://openalex.org/S41034432","display_name":"Quantum Information and Computation","issn_l":"1533-7146","issn":["1533-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322612","host_organization_name":"Rinton Press","host_organization_lineage":["https://openalex.org/P4310322612"],"host_organization_lineage_names":["Rinton Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1307.0836","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.0836","pdf_url":"https://arxiv.org/pdf/1307.0836","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1934943886","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1307.0836.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.745.5392","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.5392","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1307.0836.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1307.0836","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1307.0836","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1307.0836","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.0836","pdf_url":"https://arxiv.org/pdf/1307.0836","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332178","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1934943886.pdf","grobid_xml":"https://content.openalex.org/works/W1934943886.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1669113757","https://openalex.org/W1973585392","https://openalex.org/W1985875391","https://openalex.org/W2036265926","https://openalex.org/W2104952158","https://openalex.org/W2105259569","https://openalex.org/W2110587578","https://openalex.org/W2132833274","https://openalex.org/W2148888468","https://openalex.org/W2152144666","https://openalex.org/W2394946564","https://openalex.org/W2912318510"],"related_works":["https://openalex.org/W3118972506","https://openalex.org/W2950285192","https://openalex.org/W1539416635","https://openalex.org/W2913327613","https://openalex.org/W54371681","https://openalex.org/W2027602125","https://openalex.org/W1553290931","https://openalex.org/W2789687033","https://openalex.org/W2949259551","https://openalex.org/W129930684","https://openalex.org/W1600636537","https://openalex.org/W2764248145","https://openalex.org/W3113290665","https://openalex.org/W1668550623","https://openalex.org/W2799335769","https://openalex.org/W2068178000","https://openalex.org/W1532784182","https://openalex.org/W1947815668","https://openalex.org/W2404289303","https://openalex.org/W3048669164"],"abstract_inverted_index":{"It":[0],"is":[1,9,41,54,82],"well-known":[2],"that":[3,70,103],"deciding":[4,19,47,71,88],"equivalence":[5,21,73,90],"of":[6,18,22,46,74,87],"logic":[7],"circuits":[8,76],"a":[10,14],"coNP-complete":[11],"problem.":[12],"As":[13],"corollary,":[15],"the":[16,31,39,51,79,105],"problem":[17],"weak":[20],"reversible":[23,75,96],"circuits,":[24],"\\emph{i.e.}":[25],"allowing":[26],"initialized":[27],"ancilla":[28,36,52],"bits":[29,37],"in":[30,38],"input":[32],"and":[33,57],"ignoring":[34],"``garbage''":[35],"output,":[40],"also":[42],"coNP-complete.":[43,83],"The":[44],"complexity":[45],"strong":[48,72,89],"equivalence,":[49],"including":[50,99],"bits,":[53],"less":[55],"obvious":[56],"may":[58],"depend":[59],"on":[60],"gate":[61,81,97,101],"set.":[62],"Here":[63],"we":[64],"use":[65],"Barrington's":[66],"theorem":[67],"to":[68],"show":[69],"built":[77],"from":[78],"Fredkin":[80,108],"This":[84],"implies":[85],"coNP-completeness":[86],"for":[91],"other":[92],"commonly":[93],"used":[94],"universal":[95],"sets,":[98],"any":[100],"set":[102],"includes":[104],"Toffoli":[106],"or":[107],"gate.":[109]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}
