{"id":"https://openalex.org/W1969089240","doi":"https://doi.org/10.1109/cdc.2007.4435013","title":"Solving commutative relaxations of word problems","display_name":"Solving commutative relaxations of word problems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1969089240","doi":"https://doi.org/10.1109/cdc.2007.4435013","mag":"1969089240"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4435013","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4435013","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-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/A5033777007","display_name":"Danielle C. Tarraf","orcid":"https://orcid.org/0000-0002-9141-1870"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I117023288","display_name":"Analog Devices (United States)","ror":"https://ror.org/01545pm61","country_code":"US","type":"company","lineage":["https://openalex.org/I117023288"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Danielle C. Tarraf","raw_affiliation_strings":["Division of Control and Dynamical Systems, Cambridge Analog Technologies, Inc., Bedford, MA, USA","Caltech, Pasadena"],"affiliations":[{"raw_affiliation_string":"Division of Control and Dynamical Systems, Cambridge Analog Technologies, Inc., Bedford, MA, USA","institution_ids":["https://openalex.org/I117023288"]},{"raw_affiliation_string":"Caltech, Pasadena","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031935416","display_name":"Pablo A. Parrilo","orcid":"https://orcid.org/0000-0003-1132-8477"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":["Electrical Engineering and Computer Science Department, MIT, Cambridge, MA, USA","Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering and Computer Science Department, MIT, Cambridge, MA, USA","institution_ids":[]},{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033777007"],"corresponding_institution_ids":["https://openalex.org/I117023288","https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0693482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"b","issue":null,"first_page":"5575","last_page":"5580"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9980999827384949,"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":0.9980999827384949,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.996399998664856,"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/T11567","display_name":"semigroups and automata theory","score":0.9962000250816345,"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/commutative-property","display_name":"Commutative property","score":0.8311639428138733},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.8097019195556641},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.7114342451095581},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.5873960852622986},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5596508383750916},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.544257640838623},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5299357771873474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5294052362442017},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5199924111366272},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4922570288181305},{"id":"https://openalex.org/keywords/reachability-problem","display_name":"Reachability problem","score":0.47249212861061096},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38638079166412354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32626011967658997},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32247138023376465},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27678370475769043},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18627917766571045},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11752879619598389},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0710831880569458}],"concepts":[{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.8311639428138733},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8097019195556641},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.7114342451095581},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.5873960852622986},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5596508383750916},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.544257640838623},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5299357771873474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5294052362442017},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5199924111366272},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4922570288181305},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.47249212861061096},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38638079166412354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32626011967658997},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32247138023376465},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27678370475769043},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18627917766571045},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11752879619598389},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0710831880569458},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2007.4435013","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4435013","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:authors.library.caltech.edu:20421","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/20421/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W40978292","https://openalex.org/W1966307150","https://openalex.org/W1989763544","https://openalex.org/W1989788631","https://openalex.org/W2004459113","https://openalex.org/W2004746351","https://openalex.org/W2011495892","https://openalex.org/W2013504313","https://openalex.org/W2066594542","https://openalex.org/W2077725083","https://openalex.org/W2121161036","https://openalex.org/W2912818154","https://openalex.org/W4238858352","https://openalex.org/W6759055872"],"related_works":["https://openalex.org/W1507516107","https://openalex.org/W2047831585","https://openalex.org/W4253760428","https://openalex.org/W3208672221","https://openalex.org/W3017277461","https://openalex.org/W2099490078","https://openalex.org/W4287199681","https://openalex.org/W3172202899","https://openalex.org/W1548979236","https://openalex.org/W4224983736"],"abstract_inverted_index":{"We":[0,20,37,64],"present":[1],"an":[2],"algebraic":[3],"characterization":[4],"of":[5,10,16,25,48,69],"the":[6,11,26,33],"standard":[7],"commutative":[8,27,49],"relaxation":[9],"word":[12,28,50],"problem":[13,41],"in":[14],"terms":[15],"a":[17,23,45,67],"polynomial":[18],"equality.":[19],"then":[21],"consider":[22],"variant":[24],"problem,":[29],"referred":[30],"to":[31,44,57],"as":[32],"\"zero-to-all":[34],"reachability\"":[35],"problem.":[36],"show":[38],"that":[39],"this":[40,55],"is":[42],"equivalent":[43],"finite":[46],"number":[47],"problems,":[51],"and":[52],"we":[53],"use":[54],"insight":[56],"derive":[58],"necessary":[59],"conditions":[60],"for":[61],"zero-to-all":[62],"reachability.":[63],"conclude":[65],"with":[66],"set":[68],"illustrative":[70],"examples.":[71]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
