{"id":"https://openalex.org/W2800575014","doi":"https://doi.org/10.1109/lics.2019.8785754","title":"A Generic Normal Form for ZX-Diagrams and Application to the Rational Angle Completeness","display_name":"A Generic Normal Form for ZX-Diagrams and Application to the Rational Angle Completeness","publication_year":2019,"publication_date":"2019-06-01","ids":{"openalex":"https://openalex.org/W2800575014","doi":"https://doi.org/10.1109/lics.2019.8785754","mag":"2800575014"},"language":"en","primary_location":{"id":"doi:10.1109/lics.2019.8785754","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2019.8785754","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1805.05296","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020089810","display_name":"Emmanuel Jeandel","orcid":"https://orcid.org/0000-0001-7236-2906"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Emmanuel Jeandel","raw_affiliation_strings":["CNRS, Universit\u00e9 de Lorraine, Nancy, France","CNRS, Inria, LORIA, Universit\u00e9 de Lorraine, Nancy, F54000, France"],"affiliations":[{"raw_affiliation_string":"CNRS, Universit\u00e9 de Lorraine, Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, Inria, LORIA, Universit\u00e9 de Lorraine, Nancy, F54000, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I4210121838","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029014455","display_name":"Simon Perdrix","orcid":"https://orcid.org/0000-0002-1808-2409"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Simon Perdrix","raw_affiliation_strings":["CNRS, Universit\u00e9 de Lorraine, Nancy, France","CNRS, Inria, LORIA, Universit\u00e9 de Lorraine, Nancy, F54000, France"],"affiliations":[{"raw_affiliation_string":"CNRS, Universit\u00e9 de Lorraine, Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, Inria, LORIA, Universit\u00e9 de Lorraine, Nancy, F54000, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I4210121838","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060401218","display_name":"Renaud Vilmart","orcid":"https://orcid.org/0000-0002-8828-4671"},"institutions":[{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Renaud Vilmart","raw_affiliation_strings":["CNRS, Universit\u00e9 de Lorraine, Nancy, France","CNRS, Inria, LORIA, Universit\u00e9 de Lorraine, Nancy, F54000, France"],"affiliations":[{"raw_affiliation_string":"CNRS, Universit\u00e9 de Lorraine, Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, Inria, LORIA, Universit\u00e9 de Lorraine, Nancy, F54000, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I4210121838","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020089810"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I90183372"],"apc_list":null,"apc_paid":null,"fwci":0.1447,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54536399,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9984999895095825,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9984999895095825,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.998199999332428,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/fragment","display_name":"Fragment (logic)","score":0.8480035066604614},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.8219937086105347},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.751175045967102},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6046895980834961},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.591460108757019},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5266194939613342},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4675024747848511},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3953756093978882},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3350796699523926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2571406364440918},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11742258071899414},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09906917810440063},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09303152561187744},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07345694303512573},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.0644264817237854}],"concepts":[{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.8480035066604614},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.8219937086105347},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.751175045967102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6046895980834961},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.591460108757019},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5266194939613342},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4675024747848511},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3953756093978882},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3350796699523926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2571406364440918},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11742258071899414},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09906917810440063},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09303152561187744},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07345694303512573},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0644264817237854},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/lics.2019.8785754","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2019.8785754","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1805.05296","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.05296","pdf_url":"https://arxiv.org/pdf/1805.05296","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":null,"raw_type":"text"},{"id":"mag:2800575014","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1805.05296.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:HAL:hal-01791791v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01791791","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"LICS 2019 - 34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. &#x27E8;10.1109/LICS.2019.8785754&#x27E9;","raw_type":"Conference papers"},{"id":"doi:10.48550/arxiv.1805.05296","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1805.05296","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:1805.05296","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.05296","pdf_url":"https://arxiv.org/pdf/1805.05296","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2800575014.pdf","grobid_xml":"https://content.openalex.org/works/W2800575014.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W32507011","https://openalex.org/W1486765721","https://openalex.org/W1617295181","https://openalex.org/W1656783145","https://openalex.org/W1826773490","https://openalex.org/W1925988739","https://openalex.org/W1974928788","https://openalex.org/W2096331363","https://openalex.org/W2097264545","https://openalex.org/W2102162525","https://openalex.org/W2144309163","https://openalex.org/W2288446724","https://openalex.org/W2610243179","https://openalex.org/W2618835066","https://openalex.org/W2623710274","https://openalex.org/W2758270599","https://openalex.org/W2798910219","https://openalex.org/W2950843936","https://openalex.org/W2951006309","https://openalex.org/W2963618180","https://openalex.org/W2964268018","https://openalex.org/W2990961515","https://openalex.org/W3029808119","https://openalex.org/W3099483219","https://openalex.org/W3101982630","https://openalex.org/W3103730115","https://openalex.org/W3104500086","https://openalex.org/W3105021321","https://openalex.org/W6682769612","https://openalex.org/W6740873839","https://openalex.org/W6750625462","https://openalex.org/W6750940941","https://openalex.org/W6785470452"],"related_works":["https://openalex.org/W2966537942","https://openalex.org/W2050811372","https://openalex.org/W3204553115","https://openalex.org/W2088350978","https://openalex.org/W2467982476","https://openalex.org/W1808099261","https://openalex.org/W2084443499","https://openalex.org/W2955479224","https://openalex.org/W3101258384","https://openalex.org/W2951927819","https://openalex.org/W1967382676","https://openalex.org/W2772712032","https://openalex.org/W2115998135","https://openalex.org/W2024841767","https://openalex.org/W1999522767","https://openalex.org/W2964307513","https://openalex.org/W2951046429","https://openalex.org/W1598835176","https://openalex.org/W12716309","https://openalex.org/W1003225912"],"abstract_inverted_index":{"Recent":[0],"completeness":[1],"results":[2,72],"on":[3],"the":[4,11,28,65,74,78,87,100],"ZX-calculus":[5,80],"used":[6],"a":[7,14,36,115],"third-party":[8],"language,":[9],"namely":[10],"ZW-Calculus.":[12],"As":[13],"consequence,":[15],"these":[16,71],"proofs":[17],"are":[18],"elegant,":[19],"but":[20,89],"sadly":[21],"non-constructive.":[22],"We":[23,50],"address":[24],"this":[25],"issue":[26],"in":[27,42],"following.":[29],"To":[30],"do":[31],"so,":[32],"we":[33,69,84,97],"first":[34],"describe":[35],"generic":[37],"normal":[38,66],"form":[39],"for":[40,54,82,91,102,107],"ZX-diagrams":[41],"any":[43,92,108],"fragment":[44,76,93,109],"that":[45,99,114],"contains":[46],"Clifford+T":[47,75,103],"quantum":[48],"mechanics.":[49],"give":[51],"sufficient":[52,124],"conditions":[53],"an":[55,61],"axiomatisation":[56,101],"to":[57,63,73],"be":[58],"complete,":[59],"and":[60,77,113,123],"algorithm":[62],"reach":[64],"form.":[67],"Finally,":[68],"apply":[70],"general":[79],"-":[81],"which":[83],"already":[85],"know":[86],"completeness-,":[88],"also":[90,105],"of":[94,110],"rational":[95],"angles:":[96],"show":[98],"is":[104,121],"complete":[106],"dyadic":[111],"angles,":[112],"simple":[116],"new":[117],"rule":[118],"(called":[119],"cancellation)":[120],"necessary":[122],"otherwise.":[125]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2022-10-02T00:00:00"}
