{"id":"https://openalex.org/W2786244858","doi":"https://doi.org/10.1002/malq.201800068","title":"Parametric Presburger arithmetic: complexity of counting and quantifier elimination","display_name":"Parametric Presburger arithmetic: complexity of counting and quantifier elimination","publication_year":2019,"publication_date":"2019-09-01","ids":{"openalex":"https://openalex.org/W2786244858","doi":"https://doi.org/10.1002/malq.201800068","mag":"2786244858"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201800068","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.201800068","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.201800068","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.201800068","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011954680","display_name":"Tristram Bogart","orcid":"https://orcid.org/0000-0002-1589-8584"},"institutions":[{"id":"https://openalex.org/I162096671","display_name":"Universidad de Los Andes","ror":"https://ror.org/02mhbdp94","country_code":"CO","type":"education","lineage":["https://openalex.org/I162096671"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Tristram Bogart","raw_affiliation_strings":["Departamento de Matem\u00e1ticas Universidad de Los Andes Carrera 1 No. 18a 10 111711 Bogot\u00e1 Colombia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas Universidad de Los Andes Carrera 1 No. 18a 10 111711 Bogot\u00e1 Colombia","institution_ids":["https://openalex.org/I162096671"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009248797","display_name":"John Goodrick","orcid":"https://orcid.org/0000-0002-3256-1035"},"institutions":[{"id":"https://openalex.org/I162096671","display_name":"Universidad de Los Andes","ror":"https://ror.org/02mhbdp94","country_code":"CO","type":"education","lineage":["https://openalex.org/I162096671"]}],"countries":["CO"],"is_corresponding":true,"raw_author_name":"John Goodrick","raw_affiliation_strings":["Departamento de Matem\u00e1ticas Universidad de Los Andes Carrera 1 No. 18a 10 111711 Bogot\u00e1 Colombia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas Universidad de Los Andes Carrera 1 No. 18a 10 111711 Bogot\u00e1 Colombia","institution_ids":["https://openalex.org/I162096671"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007318007","display_name":"Danny Nguyen","orcid":"https://orcid.org/0000-0002-1695-4242"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Danny Nguyen","raw_affiliation_strings":["Department of Mathematics University of Michigan Ann Arbor, 530 Church Street Ann Arbor MI 48109\u20101043 United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Michigan Ann Arbor, 530 Church Street Ann Arbor MI 48109\u20101043 United States of America","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008278795","display_name":"Kevin M. Woods","orcid":"https://orcid.org/0000-0002-0198-6129"},"institutions":[{"id":"https://openalex.org/I70571728","display_name":"Oberlin College","ror":"https://ror.org/05ac26z88","country_code":"US","type":"education","lineage":["https://openalex.org/I70571728"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kevin Woods","raw_affiliation_strings":["Department of Mathematics Oberlin College 10 N. Professor St. Oberlin OH 44074 United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Oberlin College 10 N. Professor St. Oberlin OH 44074 United States of America","institution_ids":["https://openalex.org/I70571728"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009248797"],"corresponding_institution_ids":["https://openalex.org/I162096671"],"apc_list":{"value":2500,"currency":"USD","value_usd":2500},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01430564,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"2","first_page":"237","last_page":"250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9973000288009644,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9957000017166138,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9796000123023987,"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/presburger-arithmetic","display_name":"Presburger arithmetic","score":0.8301185965538025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.679745078086853},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6473572254180908},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5932650566101074},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.5286536812782288},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48444536328315735},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4401390552520752},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.4229952394962311},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4135708212852478},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.4102005958557129},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.1050766110420227},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09848108887672424}],"concepts":[{"id":"https://openalex.org/C5852641","wikidata":"https://www.wikidata.org/wiki/Q956059","display_name":"Presburger arithmetic","level":3,"score":0.8301185965538025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.679745078086853},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6473572254180908},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5932650566101074},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.5286536812782288},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48444536328315735},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4401390552520752},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.4229952394962311},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4135708212852478},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.4102005958557129},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.1050766110420227},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09848108887672424},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":5,"locations":[{"id":"doi:10.1002/malq.201800068","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.201800068","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.201800068","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1802.00974","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.00974","pdf_url":"https://arxiv.org/pdf/1802.00974","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:2786244858","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1802.00974.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:deepblue.lib.umich.edu:2027.42/151911","is_oa":false,"landing_page_url":"https://hdl.handle.net/2027.42/151911","pdf_url":null,"source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"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":"Article"},{"id":"doi:10.48550/arxiv.1802.00974","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.00974","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.1002/malq.201800068","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.201800068","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.201800068","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309305","display_name":"San Francisco State University","ror":"https://ror.org/05ykr0121"},{"id":"https://openalex.org/F4320332502","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2786244858.pdf","grobid_xml":"https://content.openalex.org/works/W2786244858.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1987803410","https://openalex.org/W2004193076","https://openalex.org/W2008770192","https://openalex.org/W2082494602","https://openalex.org/W2129740858","https://openalex.org/W2133174951","https://openalex.org/W2323777246","https://openalex.org/W2502236103","https://openalex.org/W2962897604","https://openalex.org/W2963706602","https://openalex.org/W3098542245","https://openalex.org/W4293765673","https://openalex.org/W6682831944"],"related_works":["https://openalex.org/W2971435283","https://openalex.org/W3098542245","https://openalex.org/W2005868382","https://openalex.org/W3129328269","https://openalex.org/W2952783120","https://openalex.org/W247209993","https://openalex.org/W2913904462","https://openalex.org/W2579801771","https://openalex.org/W1205694693","https://openalex.org/W2963570027","https://openalex.org/W2020505980","https://openalex.org/W2951829047","https://openalex.org/W2067375329","https://openalex.org/W2942073256","https://openalex.org/W3037199564","https://openalex.org/W2137828924","https://openalex.org/W2951405814","https://openalex.org/W2972131259","https://openalex.org/W3045417474","https://openalex.org/W3092687058"],"abstract_inverted_index":{"Abstract":[0],"We":[1,77],"consider":[2],"an":[3,51],"expansion":[4],"of":[5,37,71,137],"Presburger":[6],"arithmetic":[7],"which":[8],"allows":[9],"multiplication":[10],"by":[11],"k":[12],"parameters":[13],".":[14,108],"A":[15],"formula":[16],"in":[17,26,119,134,140],"this":[18],"language":[19,122],"defines":[20],"a":[21,35,40,56,81,96,120],"parametric":[22,97,112],"set":[23,98],"as":[24,34,50],"varies":[25],",":[27],"and":[28,139,148],"we":[29,94,127],"examine":[30],"the":[31,65,72,124,135,146],"counting":[32],"function":[33,36,66],"t.":[38],"For":[39],"single":[41],"parameter,":[42],"it":[43],"is":[44,55,67,84,101,130],"known":[45],"that":[46,79,100,129],"can":[47,142],"be":[48,143],"expressed":[49],"eventual":[52],"quasi\u2010polynomial":[53],"(there":[54],"period":[57],"m":[58],"such":[59,80,99],"that,":[60],"for":[61,111],"sufficiently":[62],"large":[63],"t,":[64,138],"polynomial":[68],"on":[69,106],"each":[70],"residue":[73],"classes":[74],"mod":[75],"m).":[76],"show":[78,128],"nice":[82],"expression":[83],"impossible":[85],"with":[86,114],"2":[87],"or":[88],"more":[89],"parameters.":[90],"Indeed":[91],"(assuming":[92],")":[93],"construct":[95],"not":[102],"even":[103],"polynomial\u2010time":[104,132],"computable":[105,133],"input":[107],"In":[109],"contrast,":[110],"sets":[113],"arbitrarily":[115],"many":[116],"parameters,":[117],"defined":[118],"similar":[121,149],"without":[123],"ordering":[125],"relation,":[126],"always":[131],"size":[136],"fact":[141],"represented":[144],"using":[145],"gcd":[147],"functions.":[150]},"counts_by_year":[],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2022-10-06T00:00:00"}
