{"id":"https://openalex.org/W2784624970","doi":"https://doi.org/10.23638/lmcs-15(1:34)2019","title":"Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture","display_name":"Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture","publication_year":2019,"publication_date":"2019-03-29","ids":{"openalex":"https://openalex.org/W2784624970","doi":"https://doi.org/10.23638/lmcs-15(1:34)2019","mag":"2784624970"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-15(1:34)2019","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-15(1:34)2019","pdf_url":"https://lmcs.episciences.org/5328/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/5328/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085623977","display_name":"Predrag Jani\u010di\u0107","orcid":"https://orcid.org/0000-0001-8922-4948"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Predrag Jani\u010di\u0107","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8922-4948","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103231254","display_name":"Filip Mari\u0107","orcid":"https://orcid.org/0000-0001-7219-6960"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Filip Mari\u0107","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083436657","display_name":"Marko Malikovi\u0107","orcid":"https://orcid.org/0000-0001-8333-0651"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marko Malikovi\u0107","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085623977"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00381612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Volume 15, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9984999895095825,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9984999895095825,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9750999808311462,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9575999975204468,"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/chess-endgame","display_name":"Chess endgame","score":0.9032289981842041},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8489866256713867},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.7139760255813599},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.6827117204666138},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6479864120483398},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.616568386554718},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42968830466270447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3690585494041443},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3424815833568573},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2843972444534302},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19782754778862}],"concepts":[{"id":"https://openalex.org/C118491383","wikidata":"https://www.wikidata.org/wiki/Q332225","display_name":"Chess endgame","level":2,"score":0.9032289981842041},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8489866256713867},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7139760255813599},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.6827117204666138},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6479864120483398},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.616568386554718},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42968830466270447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3690585494041443},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3424815833568573},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2843972444534302},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19782754778862},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23638/lmcs-15(1:34)2019","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-15(1:34)2019","pdf_url":"https://lmcs.episciences.org/5328/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1801.07528","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.07528","pdf_url":"https://arxiv.org/pdf/1801.07528","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1801.07528","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.07528","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:2964272612","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1801.07528.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":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"doi:10.23638/lmcs-15(1:34)2019","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-15(1:34)2019","pdf_url":"https://lmcs.episciences.org/5328/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2784624970.pdf","grobid_xml":"https://content.openalex.org/works/W2784624970.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W44728454","https://openalex.org/W59105887","https://openalex.org/W81349459","https://openalex.org/W146121977","https://openalex.org/W202807205","https://openalex.org/W319386043","https://openalex.org/W836593775","https://openalex.org/W1459875537","https://openalex.org/W1495665224","https://openalex.org/W1514486135","https://openalex.org/W1521417784","https://openalex.org/W1523712082","https://openalex.org/W1526216923","https://openalex.org/W1526604233","https://openalex.org/W1528908721","https://openalex.org/W1552715853","https://openalex.org/W1574010314","https://openalex.org/W1976969390","https://openalex.org/W1995987707","https://openalex.org/W2009007175","https://openalex.org/W2012978749","https://openalex.org/W2022589543","https://openalex.org/W2045196404","https://openalex.org/W2066661540","https://openalex.org/W2074364057","https://openalex.org/W2082217430","https://openalex.org/W2106192381","https://openalex.org/W2125967324","https://openalex.org/W2139659782","https://openalex.org/W2140583545","https://openalex.org/W2148169424","https://openalex.org/W2149534079","https://openalex.org/W2156433885","https://openalex.org/W2249204130","https://openalex.org/W2344153918","https://openalex.org/W2558199011","https://openalex.org/W2575502164","https://openalex.org/W2593442906","https://openalex.org/W2604202109","https://openalex.org/W2741018536","https://openalex.org/W2753309515","https://openalex.org/W2963864435","https://openalex.org/W2964077831"],"related_works":["https://openalex.org/W54267352","https://openalex.org/W2786801901","https://openalex.org/W2955468987","https://openalex.org/W1517387034","https://openalex.org/W2002491919","https://openalex.org/W2536541347","https://openalex.org/W23628338","https://openalex.org/W2108021684","https://openalex.org/W55831818","https://openalex.org/W2506223861"],"abstract_inverted_index":{"There":[0],"are":[1],"several":[2],"approaches":[3,77],"for":[4,23,34,55,78,97],"using":[5,20],"computers":[6],"in":[7,45,57,86],"deriving":[8,103],"mathematical":[9],"proofs.":[10,105],"For":[11],"their":[12],"illustration,":[13],"we":[14],"provide":[15],"an":[16],"in-depth":[17],"study":[18],"of":[19,31],"computer":[21],"support":[22],"proving":[24,81],"one":[25],"complex":[26,104],"combinatorial":[27],"conjecture":[28],"--":[29],"correctness":[30],"a":[32,52],"strategy":[33,54],"the":[35,58,90],"chess":[36],"KRK":[37,59],"endgame.":[38],"The":[39],"final,":[40],"machine":[41],"verifiable,":[42],"result":[43],"presented":[44],"this":[46],"paper":[47],"is":[48,51,94],"that":[49,75,89],"there":[50],"winning":[53],"white":[56],"endgame":[60],"generalized":[61],"to":[62,101],"$n":[63],"\\times":[64],"n$":[65],"board":[66],"(for":[67],"natural":[68],"$n$":[69],"greater":[70],"than":[71],"$3$).":[72],"We":[73],"demonstrate":[74],"different":[76],"computer-based":[79],"theorem":[80],"work":[82],"best":[83],"together":[84],"and":[85,88],"synergy":[87],"technology":[91],"currently":[92],"available":[93],"powerful":[95],"enough":[96],"providing":[98],"significant":[99],"help":[100],"humans":[102]},"counts_by_year":[],"updated_date":"2026-03-12T06:13:28.667946","created_date":"2025-10-10T00:00:00"}