{"id":"https://openalex.org/W2474840350","doi":"https://doi.org/10.1145/3060144","title":"Uniqueness of Normal Forms for Shallow Term Rewrite Systems","display_name":"Uniqueness of Normal Forms for Shallow Term Rewrite Systems","publication_year":2017,"publication_date":"2017-04-30","ids":{"openalex":"https://openalex.org/W2474840350","doi":"https://doi.org/10.1145/3060144","mag":"2474840350"},"language":"en","primary_location":{"id":"doi:10.1145/3060144","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3060144","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","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/1607.00431","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002782523","display_name":"Nicholas R. Radcliffe","orcid":null},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nicholas R. Radcliffe","raw_affiliation_strings":["University of Houston"],"affiliations":[{"raw_affiliation_string":"University of Houston","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059190978","display_name":"Luis F. T. Moraes","orcid":"https://orcid.org/0000-0002-2643-8647"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luis F. T. Moraes","raw_affiliation_strings":["University of Houston"],"affiliations":[{"raw_affiliation_string":"University of Houston","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050592031","display_name":"Rakesh Verma","orcid":"https://orcid.org/0000-0002-7466-7823"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rakesh M. Verma","raw_affiliation_strings":["University of Houston"],"affiliations":[{"raw_affiliation_string":"University of Houston","institution_ids":["https://openalex.org/I44461941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002782523"],"corresponding_institution_ids":["https://openalex.org/I44461941"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.004198,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"2","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9962999820709229,"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":0.9914000034332275,"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/undecidable-problem","display_name":"Undecidable problem","score":0.977348804473877},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.9619578123092651},{"id":"https://openalex.org/keywords/confluence","display_name":"Confluence","score":0.8181592226028442},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7249914407730103},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7068020701408386},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.6693065762519836},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6625210046768188},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5493152737617493},{"id":"https://openalex.org/keywords/reachability-problem","display_name":"Reachability problem","score":0.49987149238586426},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4134730100631714},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39637869596481323},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30177485942840576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1833210587501526},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11327135562896729},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05628776550292969}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.977348804473877},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.9619578123092651},{"id":"https://openalex.org/C77906462","wikidata":"https://www.wikidata.org/wiki/Q1140902","display_name":"Confluence","level":2,"score":0.8181592226028442},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7249914407730103},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7068020701408386},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.6693065762519836},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6625210046768188},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5493152737617493},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.49987149238586426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4134730100631714},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39637869596481323},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30177485942840576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1833210587501526},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11327135562896729},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05628776550292969},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":4,"locations":[{"id":"doi:10.1145/3060144","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3060144","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1607.00431","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.00431","pdf_url":"https://arxiv.org/pdf/1607.00431","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:2474840350","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1607.00431.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":"doi:10.48550/arxiv.1607.00431","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1607.00431","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:1607.00431","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.00431","pdf_url":"https://arxiv.org/pdf/1607.00431","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":[{"id":"https://openalex.org/G4412377124","display_name":null,"funder_award_id":"CNS-1319212, DGE-1433817 and DUE-1241772","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2474840350.pdf","grobid_xml":"https://content.openalex.org/works/W2474840350.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W598205067","https://openalex.org/W1499960275","https://openalex.org/W1517567519","https://openalex.org/W1527100187","https://openalex.org/W1693995122","https://openalex.org/W1969777579","https://openalex.org/W2000346568","https://openalex.org/W2005822708","https://openalex.org/W2006460851","https://openalex.org/W2032122497","https://openalex.org/W2050626079","https://openalex.org/W2064236106","https://openalex.org/W2095909184","https://openalex.org/W2119045600","https://openalex.org/W2140520835","https://openalex.org/W2912818154"],"related_works":["https://openalex.org/W2119045600","https://openalex.org/W2962928105","https://openalex.org/W1551719154","https://openalex.org/W1512579902","https://openalex.org/W1485296930","https://openalex.org/W2074884184","https://openalex.org/W1507462387","https://openalex.org/W2065616401","https://openalex.org/W2021891065","https://openalex.org/W354575360","https://openalex.org/W2986248253","https://openalex.org/W1985537797","https://openalex.org/W2339589988","https://openalex.org/W2077704773","https://openalex.org/W1499505013","https://openalex.org/W1590849606","https://openalex.org/W2139500220","https://openalex.org/W2914960943","https://openalex.org/W2961332145","https://openalex.org/W2033443348"],"abstract_inverted_index":{"Uniqueness":[0],"of":[1,11,80,104,115,128],"normal":[2],"forms":[3],"(UN":[4],"=":[5,16,97],")":[6],"is":[7,17,49,86,99],"an":[8,74],"important":[9],"property":[10,48,98],"term":[12],"rewrite":[13,53,106],"systems.":[14,38,70],"UN":[15,96],"decidable":[18,34,50],"for":[19,35,51,68,101],"ground":[20],"(i.e.,":[21],"variable-free)":[22],"systems":[23,109,122],"and":[24,44,60,120],"undecidable":[25,67,100],"in":[26,55,88,110,123],"general.":[27],"Recently,":[28],"it":[29],"was":[30],"shown":[31],"to":[32,57],"be":[33],"linear,":[36],"shallow":[37,52],"We":[39,71],"generalize":[40],"this":[41,47],"previous":[42],"result":[43,85],"show":[45],"that":[46,94],"systems,":[54],"contrast":[56],"confluence,":[58],"reachability,":[59],"other":[61],"related":[62],"properties,":[63],"which":[64,111,124],"are":[65,114,127],"all":[66],"flat":[69],"also":[72],"prove":[73,93],"upper":[75],"bound":[76],"on":[77],"the":[78,95],"complexity":[79],"our":[81],"algorithm.":[82],"Our":[83],"decidability":[84],"optimal":[87],"a":[89],"sense,":[90],"since":[91],"we":[92],"two":[102,119],"classes":[103],"linear":[105],"systems:":[107],"left-flat":[108],"right-hand":[112],"sides":[113,126],"height":[116,129],"at":[117,130],"most":[118,131],"right-flat":[121],"left-hand":[125],"two.":[132]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}