{"id":"https://openalex.org/W4412898136","doi":"https://doi.org/10.1007/978-3-031-99984-0_9","title":"SMT and\u00a0Functional Equation Solving over\u00a0the\u00a0Reals: Challenges from\u00a0the\u00a0IMO","display_name":"SMT and\u00a0Functional Equation Solving over\u00a0the\u00a0Reals: Challenges from\u00a0the\u00a0IMO","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4412898136","doi":"https://doi.org/10.1007/978-3-031-99984-0_9"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-99984-0_9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-99984-0_9","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/978-3-031-99984-0_9","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031812667","display_name":"Chad E. Brown","orcid":"https://orcid.org/0000-0003-4050-4361"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chad E. Brown","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088676437","display_name":"Karel Chvalovsk\u00fd","orcid":"https://orcid.org/0000-0002-0541-3889"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karel Chvalovsk\u00fd","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083748570","display_name":"Mikol\u00e1\u0161 Janota","orcid":"https://orcid.org/0000-0003-3487-784X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mikol\u00e1\u0161 Janota","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028924645","display_name":"Miroslav Ol\u0161\u00e1k","orcid":"https://orcid.org/0000-0002-9361-1921"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mirek Ol\u0161\u00e1k","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025056965","display_name":"Stefan Ratschan","orcid":"https://orcid.org/0000-0003-1710-1513"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Ratschan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5031812667"],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32893889,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"150","last_page":"163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9972000122070312,"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":0.9972000122070312,"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":0.9962000250816345,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.967199981212616,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7712559700012207},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4157665967941284},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3849859833717346},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3510177433490753},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35087087750434875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14787009358406067},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10888931155204773}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7712559700012207},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4157665967941284},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3849859833717346},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3510177433490753},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35087087750434875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14787009358406067},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10888931155204773}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-99984-0_9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-99984-0_9","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-99984-0_9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-99984-0_9","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1781094","https://openalex.org/W1480909796","https://openalex.org/W1481397690","https://openalex.org/W1501503542","https://openalex.org/W1511737804","https://openalex.org/W1536511644","https://openalex.org/W1570787829","https://openalex.org/W2007074311","https://openalex.org/W2016056788","https://openalex.org/W2044458395","https://openalex.org/W2055477538","https://openalex.org/W2094878426","https://openalex.org/W2098095758","https://openalex.org/W2104715607","https://openalex.org/W2105315191","https://openalex.org/W2155330305","https://openalex.org/W2259620693","https://openalex.org/W2417863416","https://openalex.org/W2787155581","https://openalex.org/W2795154181","https://openalex.org/W2883018030","https://openalex.org/W3118899654","https://openalex.org/W3138477645","https://openalex.org/W3164961132","https://openalex.org/W4225922019","https://openalex.org/W4241540767","https://openalex.org/W4379193089","https://openalex.org/W4382763225","https://openalex.org/W4386363590","https://openalex.org/W4389011534","https://openalex.org/W4400169047","https://openalex.org/W6604294993","https://openalex.org/W6818100936","https://openalex.org/W6912219847"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Abstract":[0],"We":[1,64],"use":[2],"SMT":[3,58,70],"technology":[4],"to":[5,40,44,68],"address":[6],"a":[7],"class":[8],"of":[9],"problems":[10,23,52],"involving":[11],"uninterpreted":[12,48],"functions":[13],"and":[14],"nonlinear":[15],"real":[16],"arithmetic.":[17],"In":[18],"particular,":[19],"we":[20],"focus":[21],"on":[22,46],"commonly":[24],"found":[25],"in":[26,72],"mathematical":[27],"competitions,":[28],"such":[29],"as":[30],"the":[31,37],"International":[32],"Mathematical":[33],"Olympiad":[34],"(IMO),":[35],"where":[36],"task":[38],"is":[39],"determine":[41],"all":[42],"solutions":[43],"constraints":[45],"an":[47],"function.":[49],"Although":[50],"these":[51],"require":[53],"only":[54],"high-school-level":[55],"mathematics,":[56],"state-of-the-art":[57],"solvers":[59],"often":[60],"struggle":[61],"with":[62],"them.":[63],"propose":[65],"several":[66],"techniques":[67],"improve":[69],"performance":[71],"this":[73],"setting.":[74]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
