{"id":"https://openalex.org/W1568736152","doi":"https://doi.org/10.1007/3-540-51517-8_151","title":"A critical pair criterion for completion modulo a congruence","display_name":"A critical pair criterion for completion modulo a congruence","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W1568736152","doi":"https://doi.org/10.1007/3-540-51517-8_151","mag":"1568736152"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-51517-8_151","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-51517-8_151","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5090703131","display_name":"Leo Bachmair","orcid":null},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leo Bachmair","raw_affiliation_strings":["Department of Computer Science, SUNY at Stony Brook, 11794, Stony Brook, NY, USA","SUNY AT STONY BROOK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, SUNY at Stony Brook, 11794, Stony Brook, NY, USA","institution_ids":["https://openalex.org/I59553526"]},{"raw_affiliation_string":"SUNY AT STONY BROOK","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039993352","display_name":"Nachum Dershowitz","orcid":"https://orcid.org/0000-0003-0363-2735"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nachum Dershowitz","raw_affiliation_strings":["Department of Computer Science, University of Illinois, 61801, Urbana, IL, USA","#N#\u2004University of Illinois"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois, 61801, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"#N#\u2004University of Illinois","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10512129,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"452","last_page":"453"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9958999752998352,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9912999868392944,"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/modulo","display_name":"Modulo","score":0.8984601497650146},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.7798676490783691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6815739870071411},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.424530565738678},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40260931849479675},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.35412395000457764},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.353206604719162},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3403235077857971},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2822052836418152},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20865663886070251},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13737136125564575},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11087009310722351}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8984601497650146},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.7798676490783691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6815739870071411},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.424530565738678},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40260931849479675},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.35412395000457764},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.353206604719162},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3403235077857971},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2822052836418152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20865663886070251},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13737136125564575},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11087009310722351}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-51517-8_151","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-51517-8_151","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1589182689","https://openalex.org/W1964421058","https://openalex.org/W1968386045","https://openalex.org/W2013342254","https://openalex.org/W2016433302","https://openalex.org/W2042924775","https://openalex.org/W2056016391","https://openalex.org/W4248547811","https://openalex.org/W4255293094","https://openalex.org/W6642673056"],"related_works":["https://openalex.org/W3098271706","https://openalex.org/W2559888834","https://openalex.org/W4383993728","https://openalex.org/W4302848502","https://openalex.org/W2302440404","https://openalex.org/W3049507786","https://openalex.org/W1973274341","https://openalex.org/W2017804160","https://openalex.org/W2021221230","https://openalex.org/W2778969783"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}