{"id":"https://openalex.org/W2152227274","doi":"https://doi.org/10.1155/1999/45607","title":"An Efficient Algorithm for the Calculationof Generalized Adding and Arithmetic TransformsFrom Disjoint Cubes of Boolean Functions","display_name":"An Efficient Algorithm for the Calculationof Generalized Adding and Arithmetic TransformsFrom Disjoint Cubes of Boolean Functions","publication_year":1998,"publication_date":"1998-02-05","ids":{"openalex":"https://openalex.org/W2152227274","doi":"https://doi.org/10.1155/1999/45607","mag":"2152227274"},"language":"en","primary_location":{"id":"doi:10.1155/1999/45607","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1999/45607","pdf_url":"https://downloads.hindawi.com/archive/1999/045607.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/1999/045607.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016478346","display_name":"B.J. Falkowski","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Bogdan J. Falkowski","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Block S1, Nanyang Avenue"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Block S1, Nanyang Avenue","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029335324","display_name":"Chip-Hong Chang","orcid":"https://orcid.org/0000-0002-8897-6176"},"institutions":[{"id":"https://openalex.org/I21419654","display_name":"Nanyang Polytechnic","ror":"https://ror.org/04af7ga89","country_code":"SG","type":"education","lineage":["https://openalex.org/I1280293394","https://openalex.org/I21419654"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Chip-Hong Chang","raw_affiliation_strings":["Electronics Design Centre, French Singapore Institute, Nanyang Polytechnic, 180 Ang Mo Kio Ave 8"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electronics Design Centre, French Singapore Institute, Nanyang Polytechnic, 180 Ang Mo Kio Ave 8","institution_ids":["https://openalex.org/I21419654"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016478346"],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":0.5057,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6892725,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"2","first_page":"135","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9840999841690063,"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/T10142","display_name":"Formal Methods in Verification","score":0.9840999841690063,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9706000089645386,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9670000076293945,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/disjoint-sets","display_name":"Disjoint sets","score":0.8632140159606934},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6936555504798889},{"id":"https://openalex.org/keywords/truth-table","display_name":"Truth table","score":0.5475309491157532},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5424526333808899},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.5300074815750122},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5207302570343018},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5135281682014465},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.49944138526916504},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.4727431535720825},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3898618221282959},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.38205859065055847},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3324558138847351},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.05523967742919922}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8632140159606934},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6936555504798889},{"id":"https://openalex.org/C56949724","wikidata":"https://www.wikidata.org/wiki/Q219079","display_name":"Truth table","level":2,"score":0.5475309491157532},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5424526333808899},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.5300074815750122},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5207302570343018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5135281682014465},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.49944138526916504},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.4727431535720825},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3898618221282959},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.38205859065055847},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3324558138847351},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.05523967742919922},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1155/1999/45607","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1999/45607","pdf_url":"https://downloads.hindawi.com/archive/1999/045607.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1155/1999/45607","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1999/45607","pdf_url":"https://downloads.hindawi.com/archive/1999/045607.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2152227274.pdf","grobid_xml":"https://content.openalex.org/works/W2152227274.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1494035541","https://openalex.org/W1505590927","https://openalex.org/W1528648649","https://openalex.org/W1537664757","https://openalex.org/W1539380537","https://openalex.org/W2022620445","https://openalex.org/W2043021272","https://openalex.org/W2052458714","https://openalex.org/W2083323665","https://openalex.org/W2088756815","https://openalex.org/W2089068867","https://openalex.org/W2099412448","https://openalex.org/W2124837844","https://openalex.org/W2129183345","https://openalex.org/W2140019181","https://openalex.org/W2140801749","https://openalex.org/W2143647453","https://openalex.org/W2148365209","https://openalex.org/W2158102622","https://openalex.org/W2169849462","https://openalex.org/W2312235895","https://openalex.org/W2496515839","https://openalex.org/W2520093650","https://openalex.org/W2548051471","https://openalex.org/W4213009134","https://openalex.org/W4239904061","https://openalex.org/W4404418245"],"related_works":["https://openalex.org/W4252281389","https://openalex.org/W2058288504","https://openalex.org/W3141532631","https://openalex.org/W1996276855","https://openalex.org/W2131164334","https://openalex.org/W4288044863","https://openalex.org/W2037737738","https://openalex.org/W1991822629","https://openalex.org/W3145758888","https://openalex.org/W1638821902"],"abstract_inverted_index":{"A":[0],"new":[1],"algorithm":[2],"is":[3,56],"given":[4],"that":[5,29,63],"converts":[6],"a":[7,50],"reduced":[8],"representation":[9],"of":[10,16,41,76],"Boolean":[11,42,61],"functions":[12,43,62],"in":[13,88],"the":[14,26,38,44,74,83],"form":[15],"disjoint":[17,69],"cubes":[18,70],"to":[19],"Generalized":[20],"Adding":[21,31],"and":[22,32,71],"Arithmetic":[23,33],"spectra.":[24],"Since":[25],"known":[27],"algorithms":[28],"generate":[30],"spectra":[34],"always":[35],"start":[36],"from":[37],"truth":[39],"table":[40],"method":[45,55],"presented":[46],"computes":[47],"faster":[48],"with":[49],"smaller":[51],"computer":[52],"memory.":[53],"The":[54],"extremely":[57],"efficient":[58],"for":[59],"such":[60],"are":[64],"described":[65],"by":[66],"only":[67,77],"few":[68],"it":[72],"allows":[73],"calculation":[75],"selected":[78],"spectral":[79],"coefficients,":[80],"or":[81],"all":[82],"coefficients":[84],"can":[85],"be":[86],"calculated":[87],"parallel.":[89]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
