{"id":"https://openalex.org/W2169645915","doi":"https://doi.org/10.2178/jsl/1190150028","title":"The cost of a cycle is a square","display_name":"The cost of a cycle is a square","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2169645915","doi":"https://doi.org/10.2178/jsl/1190150028","mag":"2169645915"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150028","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150028","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5038174177","display_name":"Alessandra Carbone","orcid":"https://orcid.org/0000-0003-2098-5743"},"institutions":[{"id":"https://openalex.org/I197681013","display_name":"Universit\u00e9 Paris-Est Cr\u00e9teil","ror":"https://ror.org/05ggc9x40","country_code":"FR","type":"education","lineage":["https://openalex.org/I197681013"]},{"id":"https://openalex.org/I2800365227","display_name":"Paris-Est Sup","ror":"https://ror.org/0268ecp52","country_code":"FR","type":"education","lineage":["https://openalex.org/I2800365227"]},{"id":"https://openalex.org/I4210151791","display_name":"Genomics (United Kingdom)","ror":"https://ror.org/053a6xa29","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210151791"]}],"countries":["FR","GB"],"is_corresponding":true,"raw_author_name":"A. Carbone","raw_affiliation_strings":["Math\u00e9matiques/Informatique, Universit\u00e9 de Paris XII, 61 Avenue Du G\u00e9n\u00e9ral De Gaulle, 94010 Cr\u00e9teil Cedex, France, E-mail:","Analytical Genomics [LCQB]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Math\u00e9matiques/Informatique, Universit\u00e9 de Paris XII, 61 Avenue Du G\u00e9n\u00e9ral De Gaulle, 94010 Cr\u00e9teil Cedex, France, E-mail:","institution_ids":["https://openalex.org/I197681013","https://openalex.org/I2800365227"]},{"raw_affiliation_string":"Analytical Genomics [LCQB]","institution_ids":["https://openalex.org/I4210151791"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038174177"],"corresponding_institution_ids":["https://openalex.org/I197681013","https://openalex.org/I2800365227","https://openalex.org/I4210151791"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.5771,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.87671892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"67","issue":"1","first_page":"35","last_page":"60"},"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9976999759674072,"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":0.9926999807357788,"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/sequent-calculus","display_name":"Sequent calculus","score":0.7951667308807373},{"id":"https://openalex.org/keywords/cut-elimination-theorem","display_name":"Cut-elimination theorem","score":0.6497848033905029},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.6214471459388733},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.6050536036491394},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6043052077293396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5434248447418213},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5235585570335388},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5167335867881775},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.4991874694824219},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.46453148126602173},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.43039774894714355},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41798728704452515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34803617000579834},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3436363637447357},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.11440280079841614}],"concepts":[{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.7951667308807373},{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.6497848033905029},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.6214471459388733},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.6050536036491394},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6043052077293396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5434248447418213},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5235585570335388},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5167335867881775},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.4991874694824219},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.46453148126602173},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.43039774894714355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41798728704452515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34803617000579834},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3436363637447357},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.11440280079841614},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2178/jsl/1190150028","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150028","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.8852","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.8852","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.univ-paris12.fr/lacl/ale/cycles.ps.gz","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1190150028","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150028","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"pmh:oai:HAL:hal-03911649v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03911649","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Journal of Symbolic Logic, 2002, 67 (1), pp.35-60. ⟨10.2178/jsl/1190150028⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W648914933","https://openalex.org/W1547759477","https://openalex.org/W1871626709","https://openalex.org/W1970822788","https://openalex.org/W1988083342","https://openalex.org/W1990529320","https://openalex.org/W1992153273","https://openalex.org/W2014024837","https://openalex.org/W2037971976","https://openalex.org/W2044095368","https://openalex.org/W2044632231","https://openalex.org/W2056365917","https://openalex.org/W2069767473","https://openalex.org/W2158086914","https://openalex.org/W2593312943","https://openalex.org/W2911865844","https://openalex.org/W3039529476","https://openalex.org/W3183766709","https://openalex.org/W4238292764","https://openalex.org/W4241937850","https://openalex.org/W4245630182","https://openalex.org/W6679878532"],"related_works":["https://openalex.org/W2584381231","https://openalex.org/W2793983771","https://openalex.org/W2806893870","https://openalex.org/W2911183586","https://openalex.org/W2650704808","https://openalex.org/W3206179873","https://openalex.org/W102468273","https://openalex.org/W2071146589","https://openalex.org/W2918427073","https://openalex.org/W1597825325"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"logical":[2],"flow":[3],"graphs":[4],"of":[5,19,40,90],"sequent":[6],"calculus":[7,16],"proofs":[8],"might":[9,21],"contain":[10],"oriented":[11],"cycles.":[12],"For":[13,30],"the":[14,17,31,74,88],"predicate":[15],"elimination":[18],"cycles":[20,45,65],"be":[22],"non-elementary":[23],"and":[24,86],"this":[25],"was":[26],"shown":[27],"in":[28],"[Car96].":[29],"propositional":[32],"calculus,":[33],"we":[34],"prove":[35],"that":[36],"if":[37],"a":[38,59,67],"proof":[39,51,84,96],"k":[41],"lines":[42],"contains":[43],"n":[44],"then":[46],"there":[47,57],"exists":[48],"an":[49],"acyclic":[50],"with":[52],"(kn+1)":[53],"lines.":[54],"In":[55],"particular,":[56],"is":[58],"polynomial":[60],"time":[61],"algorithm":[62],"which":[63],"eliminates":[64],"from":[66],"proof.":[68],"These":[69],"results":[70],"are":[71],"motivated":[72],"by":[73,87],"search":[75],"for":[76,95],"general":[77],"methods":[78],"on":[79,83],"proving":[80],"lower":[81],"bounds":[82],"size":[85],"design":[89],"more":[91],"efficient":[92],"heuristic":[93],"algorithms":[94],"search.":[97]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}