{"id":"https://openalex.org/W2186100963","doi":"https://doi.org/10.29007/w5xk","title":"Data Conversion Method between a Natural Number and a Binary Tree for an Inductive Proof and Its Application","display_name":"Data Conversion Method between a Natural Number and a Binary Tree for an Inductive Proof and Its Application","publication_year":2018,"publication_date":"2018-01-23","ids":{"openalex":"https://openalex.org/W2186100963","doi":"https://doi.org/10.29007/w5xk","mag":"2186100963"},"language":"en","primary_location":{"id":"doi:10.29007/w5xk","is_oa":true,"landing_page_url":"https://doi.org/10.29007/w5xk","pdf_url":"https://easychair.org/publications/open/zfm","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://easychair.org/publications/open/zfm","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100892549","display_name":"Kazuko Takahashi","orcid":null},"institutions":[{"id":"https://openalex.org/I206011266","display_name":"Kwansei Gakuin University","ror":"https://ror.org/02qf2tx24","country_code":"JP","type":"education","lineage":["https://openalex.org/I206011266"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuko Takahashi","raw_affiliation_strings":["School of Science and Technology, Kwansei Gakuin University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science and Technology, Kwansei Gakuin University","institution_ids":["https://openalex.org/I206011266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039212599","display_name":"Shizuo Yoshimaru","orcid":null},"institutions":[{"id":"https://openalex.org/I206011266","display_name":"Kwansei Gakuin University","ror":"https://ror.org/02qf2tx24","country_code":"JP","type":"education","lineage":["https://openalex.org/I206011266"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shizuo Yoshimaru","raw_affiliation_strings":["School of Science and Technology, Kwansei Gakuin University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science and Technology, Kwansei Gakuin University","institution_ids":["https://openalex.org/I206011266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054632719","display_name":"Mizuki Goto","orcid":null},"institutions":[{"id":"https://openalex.org/I206011266","display_name":"Kwansei Gakuin University","ror":"https://ror.org/02qf2tx24","country_code":"JP","type":"education","lineage":["https://openalex.org/I206011266"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mizuki Goto","raw_affiliation_strings":["School of Science and Technology, Kwansei Gakuin University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science and Technology, Kwansei Gakuin University","institution_ids":["https://openalex.org/I206011266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039212599"],"corresponding_institution_ids":["https://openalex.org/I206011266"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00382011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":null,"first_page":"93","last_page":"77"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9991999864578247,"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":0.9991999864578247,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.998199999332428,"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/binary-tree","display_name":"Binary tree","score":0.7227332592010498},{"id":"https://openalex.org/keywords/hol","display_name":"HOL","score":0.7069273591041565},{"id":"https://openalex.org/keywords/divisibility-rule","display_name":"Divisibility rule","score":0.6705016493797302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6537693738937378},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6098445653915405},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5526514649391174},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.5467898845672607},{"id":"https://openalex.org/keywords/binary-expression-tree","display_name":"Binary expression tree","score":0.5318434238433838},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.49849653244018555},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.4746024012565613},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4672049880027771},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4222880005836487},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3705074191093445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32015693187713623},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31154632568359375},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20397403836250305},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.18748417496681213},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.10214272141456604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09961405396461487}],"concepts":[{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.7227332592010498},{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.7069273591041565},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.6705016493797302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6537693738937378},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6098445653915405},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5526514649391174},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.5467898845672607},{"id":"https://openalex.org/C166055160","wikidata":"https://www.wikidata.org/wiki/Q4913895","display_name":"Binary expression tree","level":3,"score":0.5318434238433838},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.49849653244018555},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.4746024012565613},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4672049880027771},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4222880005836487},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3705074191093445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32015693187713623},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31154632568359375},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20397403836250305},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.18748417496681213},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.10214272141456604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09961405396461487},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":3,"locations":[{"id":"doi:10.29007/w5xk","is_oa":true,"landing_page_url":"https://doi.org/10.29007/w5xk","pdf_url":"https://easychair.org/publications/open/zfm","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.417.9508","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.417.9508","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.easychair.org/publications/?page=913412999","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.434.6089","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.434.6089","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.easychair.org/publications/?page=913412999","raw_type":"text"}],"best_oa_location":{"id":"doi:10.29007/w5xk","is_oa":true,"landing_page_url":"https://doi.org/10.29007/w5xk","pdf_url":"https://easychair.org/publications/open/zfm","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2186100963.pdf","grobid_xml":"https://content.openalex.org/works/W2186100963.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W76816337","https://openalex.org/W155718886","https://openalex.org/W1494232233","https://openalex.org/W1508641834","https://openalex.org/W1534850143","https://openalex.org/W1597068544","https://openalex.org/W1603690896","https://openalex.org/W1847217253","https://openalex.org/W1915933348","https://openalex.org/W1972260728","https://openalex.org/W1982209843","https://openalex.org/W2023035194","https://openalex.org/W2035024861","https://openalex.org/W2046147156","https://openalex.org/W2067895825","https://openalex.org/W2076376787","https://openalex.org/W2076409494","https://openalex.org/W2106192381","https://openalex.org/W4242767025","https://openalex.org/W6600397670","https://openalex.org/W6605708452","https://openalex.org/W6608624883","https://openalex.org/W6614030999"],"related_works":["https://openalex.org/W4295798319","https://openalex.org/W2036229815","https://openalex.org/W1819460135","https://openalex.org/W3098927713","https://openalex.org/W2391685779","https://openalex.org/W1516654960","https://openalex.org/W4289109288","https://openalex.org/W2888810578","https://openalex.org/W4289666903","https://openalex.org/W2769609281"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"modeling":[3],"of":[4,83,99],"a":[5,10,26,32,36,52],"binary":[6,37,74],"tree":[7,38,75],"that":[8],"represents":[9],"natural":[11,33],"number":[12,34],"and":[13,39,58,76,91],"gives":[14],"an":[15,41,62],"inductive":[16,42],"proof":[17,43],"for":[18,28,44],"its":[19,45],"properties":[20],"using":[21,86],"theorem":[22,88],"provers.":[23],"We":[24,47,66],"define":[25,68],"function":[27,71],"converting":[29],"data":[30],"from":[31],"into":[35],"give":[40],"well-definedness.":[46],"formalize":[48],"this":[49,100],"method,":[50],"develop":[51],"computational":[53],"model":[54],"based":[55],"on":[56,72,78],"it,":[57],"apply":[59],"it":[60],"to":[61,79],"electronic":[63,84],"cash":[64,85],"protocol.":[65],"also":[67],"the":[69,73,81,87,97],"payment":[70],"go":[77],"prove":[80],"divisibility":[82],"provers":[89],"Isabelle/HOL":[90],"Coq,":[92],"respectively.":[93],"Furthermore,":[94],"we":[95],"discuss":[96],"effectiveness":[98],"method.":[101]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}