{"id":"https://openalex.org/W4385343018","doi":"https://doi.org/10.1134/s0361768823040102","title":"Admissible Ordering on Monomials is Well-Founded: A Constructive Proof","display_name":"Admissible Ordering on Monomials is Well-Founded: A Constructive Proof","publication_year":2023,"publication_date":"2023-07-28","ids":{"openalex":"https://openalex.org/W4385343018","doi":"https://doi.org/10.1134/s0361768823040102"},"language":"en","primary_location":{"id":"doi:10.1134/s0361768823040102","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/s0361768823040102","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Programming and Computer Software","raw_type":"journal-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/A5039848569","display_name":"S. D. Meshveliani","orcid":"https://orcid.org/0000-0002-4224-6178"},"institutions":[{"id":"https://openalex.org/I4210143630","display_name":"Program Systems Institute of RAS","ror":"https://ror.org/040r4cv22","country_code":"RU","type":"education","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210143630"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"S. D. Meshveliani","raw_affiliation_strings":["Ailamazyan Program Systems Institute, Russian Academy of Sciences, ul. Petra Pervogo 4a, 152021, s. Ves\u2019kovo, Pereslavsky District, Yaroslavl Oblast, Russia","Ailamazyan Program Systems Institute, Russian Academy of Sciences, s. Ves\u2019kovo, Russia"],"affiliations":[{"raw_affiliation_string":"Ailamazyan Program Systems Institute, Russian Academy of Sciences, ul. Petra Pervogo 4a, 152021, s. Ves\u2019kovo, Pereslavsky District, Yaroslavl Oblast, Russia","institution_ids":["https://openalex.org/I4210143630"]},{"raw_affiliation_string":"Ailamazyan Program Systems Institute, Russian Academy of Sciences, s. Ves\u2019kovo, Russia","institution_ids":["https://openalex.org/I4210143630"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039848569"],"corresponding_institution_ids":["https://openalex.org/I4210143630"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.081036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"4","first_page":"199","last_page":"214"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9991000294685364,"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":0.9991000294685364,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.996399998664856,"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/T10142","display_name":"Formal Methods in Verification","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"}}],"keywords":[{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.824142336845398},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.7794956564903259},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6136768460273743},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5883988738059998},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.48274654150009155},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.4812726378440857},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.4682866930961609},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46610578894615173},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.4518716335296631},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2798194885253906},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24192917346954346},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23204272985458374},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.0949244499206543},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07585152983665466}],"concepts":[{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.824142336845398},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7794956564903259},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6136768460273743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5883988738059998},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.48274654150009155},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.4812726378440857},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.4682866930961609},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46610578894615173},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.4518716335296631},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2798194885253906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24192917346954346},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23204272985458374},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.0949244499206543},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07585152983665466},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0361768823040102","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/s0361768823040102","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Programming and Computer Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W16315125","https://openalex.org/W569543113","https://openalex.org/W1971479478","https://openalex.org/W2007116092","https://openalex.org/W2020759317","https://openalex.org/W4242767025","https://openalex.org/W6601931442","https://openalex.org/W6814866840"],"related_works":["https://openalex.org/W2949665548","https://openalex.org/W3186402499","https://openalex.org/W1998096192","https://openalex.org/W201195458","https://openalex.org/W2950188642","https://openalex.org/W151625577","https://openalex.org/W1844192718","https://openalex.org/W1999021815","https://openalex.org/W2105747912","https://openalex.org/W2510622047"],"abstract_inverted_index":{"In":[0,33,60],"this":[1,49,96,151,174],"paper,":[2],"we":[3,111],"consider":[4],"a":[5,71,92,107,212],"constructive":[6,65,76,86,93,148],"proof":[7,94,149,175],"of":[8,11,26,39,56,78,81,95,124,135,143,150,183,187,201,214],"the":[9,12,23,36,54,57,79,82,116,122,136,164,177,181,196,202,208],"termination":[10,55,200],"normal":[13],"form":[14,182],"(NF)":[15],"algorithm":[16,204],"for":[17,99,205,217],"multivariate":[18],"polynomials,":[19],"as":[20,22,115],"well":[21],"related":[24],"concept":[25],"admissible":[27,127],"ordering":[28,83,128],"<":[29,41,100],"$$_{e}$$":[30,42,101],"on":[31,64,106,121,147],"monomials.":[32],"classical":[34],"mathematics,":[35],"well-quasiorder":[37],"property":[38],"relation":[40],"is":[43,50,88,104,129,221],"derived":[44],"from":[45,163],"Dickson\u2019s":[46],"lemma,":[47],"and":[48,69],"sufficient":[51],"to":[52,113,198,227],"justify":[53],"NF":[58,137,203],"algorithm.":[59,138],"provable":[61,188,215],"programming":[62],"based":[63,105],"type":[66],"theory":[67],"(Coq":[68],"Agda),":[70],"somewhat":[72],"stronger":[73],"condition":[74],"(in":[75,84],"mathematics)":[77],"well-foundedness":[80,123],"its":[85],"version)":[87],"required.":[89],"We":[90,139,172],"propose":[91],"theorem":[97,120,197],"(T)":[98],",":[102],"which":[103,220],"known":[108],"method":[109],"that":[110,157,225],"refer":[112],"here":[114],"\u201cpattern":[117],"method.\u201d":[118],"This":[119,192],"an":[125],"arbitrary":[126],"also":[130,194,210],"important":[131],"in":[132,170,176,180],"itself,":[133],"independently":[134],"are":[140],"not":[141,160],"aware":[142],"any":[144],"other":[145,168],"works":[146],"theorem.":[152],"However,":[153],"it":[154,158],"turns":[155],"out":[156],"follows,":[159],"very":[161],"difficultly,":[162],"results":[165],"achieved":[166],"by":[167],"researchers":[169],"2003.":[171],"program":[173],"Agda":[178],"language":[179],"our":[184],"library":[185,209],"AdmissiblePPO-wellFounded":[186],"computational":[189],"algebra":[190],"programs.":[191],"development":[193],"uses":[195],"prove":[199,228],"polynomials.":[206],"Thus,":[207],"contains":[211],"set":[213],"programs":[216],"polynomial":[218],"algebra,":[219],"significantly":[222],"larger":[223],"than":[224],"needed":[226],"Theorem":[229],"T.":[230]},"counts_by_year":[],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}