{"id":"https://openalex.org/W2762225945","doi":"https://doi.org/10.4230/lipics.mfcs.2018.18","title":"Lagrange's Theorem for Binary Squares","display_name":"Lagrange's Theorem for Binary Squares","publication_year":2017,"publication_date":"2017-10-11","ids":{"openalex":"https://openalex.org/W2762225945","doi":"https://doi.org/10.4230/lipics.mfcs.2018.18","mag":"2762225945"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:9600","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.18","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.18","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112870293","display_name":"P. Madhusudan","orcid":null},"institutions":[{"id":"https://openalex.org/I71561298","display_name":"Goodwin College","ror":"https://ror.org/009bjed14","country_code":"US","type":"education","lineage":["https://openalex.org/I71561298"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Madhusudan, P.","raw_affiliation_strings":["Department of Computer Science, Thomas M. Siebel Center for Computer Science, 201 North Goodwin Avenue, Urbana, IL 61801-2302, USA","Siebel Center for Computer Science"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Thomas M. Siebel Center for Computer Science, 201 North Goodwin Avenue, Urbana, IL 61801-2302, USA","institution_ids":["https://openalex.org/I71561298"]},{"raw_affiliation_string":"Siebel Center for Computer Science","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077221909","display_name":"Dirk Nowotka","orcid":"https://orcid.org/0000-0002-5422-2229"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Christian-Albrechts-Universit\u00e4t zu Kiel","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nowotka, Dirk","raw_affiliation_strings":["Department of Computer Science, Kiel University, D-24098 Kiel, Germany","Kiel University;"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Kiel University, D-24098 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]},{"raw_affiliation_string":"Kiel University;","institution_ids":["https://openalex.org/I32021983"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022656377","display_name":"Aayush Rajasekaran","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Rajasekaran, Aayush","raw_affiliation_strings":["School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada","University of WAterloo"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of WAterloo","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065322269","display_name":"Jeffrey Shallit","orcid":"https://orcid.org/0000-0003-1197-3820"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shallit, Jeffrey","raw_affiliation_strings":["School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada","University of WAterloo"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of WAterloo","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5112870293"],"corresponding_institution_ids":["https://openalex.org/I71561298"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17483909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"18","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9993000030517578,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9987999796867371,"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/decidability","display_name":"Decidability","score":0.8987952470779419},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7160627245903015},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.5700321793556213},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.529900848865509},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.508454442024231},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4972365200519562},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.4892570972442627},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.4853619337081909},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4166645407676697},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32300233840942383},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11376550793647766}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8987952470779419},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7160627245903015},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.5700321793556213},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.529900848865509},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.508454442024231},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4972365200519562},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.4892570972442627},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.4853619337081909},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4166645407676697},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32300233840942383},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11376550793647766},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:9600","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.18","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},{"id":"pmh:oai:arXiv.org:1710.04247","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.04247","pdf_url":"https://arxiv.org/pdf/1710.04247","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":"","raw_type":"text"},{"id":"mag:2762225945","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1710.04247.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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1710.04247","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.04247","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":null,"raw_type":"article"},{"id":"mag:2962763578","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1710.04247","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},{"id":"doi:10.4230/lipics.mfcs.2018.18","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.mfcs.2018.18","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:9600","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.18","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.699999988079071}],"awards":[{"id":"https://openalex.org/G5451691127","display_name":null,"funder_award_id":"1527395","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1484141858","https://openalex.org/W1495204714","https://openalex.org/W1568671078","https://openalex.org/W2002089154","https://openalex.org/W2055422725","https://openalex.org/W2149907859","https://openalex.org/W2328642983","https://openalex.org/W2340639842","https://openalex.org/W2767147153","https://openalex.org/W2790140360","https://openalex.org/W2793662473","https://openalex.org/W2801038635","https://openalex.org/W2964257454","https://openalex.org/W3013116335"],"related_works":["https://openalex.org/W2962763578","https://openalex.org/W2798699651","https://openalex.org/W2183198433","https://openalex.org/W2169150716","https://openalex.org/W2142744108","https://openalex.org/W2775226152","https://openalex.org/W2948267232","https://openalex.org/W1803783765","https://openalex.org/W2076678106","https://openalex.org/W2090874414","https://openalex.org/W2950038686","https://openalex.org/W2551544944","https://openalex.org/W2243954424","https://openalex.org/W2579968970","https://openalex.org/W2902951379","https://openalex.org/W1966181449","https://openalex.org/W2956865288","https://openalex.org/W2073746311","https://openalex.org/W2125429972","https://openalex.org/W2030445287"],"abstract_inverted_index":{"We":[0],"show":[1,83,98],"how":[2,99],"to":[3,105],"prove":[4],"theorems":[5],"in":[6,78,94],"additive":[7],"number":[8,31,67],"theory":[9],"using":[10],"a":[11,48,53,79],"decision":[12],"procedure":[13],"based":[14],"on":[15],"finite":[16],"automata.":[17],"Among":[18],"other":[19],"things,":[20],"we":[21,72,82],"obtain":[22],"the":[23,35,56,66,89],"following":[24],"analogue":[25],"of":[26,37,55,62],"Lagrange's":[27],"theorem:":[28],"every":[29],"natural":[30,41],">":[32],"686":[33],"is":[34,47,69],"sum":[36],"at":[38],"most":[39],"4":[40,68],"numbers":[42],"whose":[43],"canonical":[44],"base-2":[45],"representation":[46],"binary":[49],"square,":[50],"that":[51,84,87],"is,":[52],"string":[54],"form":[57],"xx":[58],"for":[59,107],"some":[60],"block":[61],"bits":[63],"x.":[64],"Here":[65],"optimal.":[70],"While":[71],"cannot":[73],"embed":[74],"this":[75],"theorem":[76,90],"itself":[77],"decidable":[80,95],"theory,":[81],"stronger":[85,109],"lemmas":[86],"imply":[88],"can":[91,102],"be":[92,103],"embedded":[93],"theories,":[96],"and":[97],"automated":[100],"methods":[101],"used":[104],"search":[106],"these":[108],"lemmas.":[110]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2022-10-04T00:00:00"}
