{"id":"https://openalex.org/W2091002049","doi":"https://doi.org/10.1109/ita.2014.6804265","title":"Parallel algorithms for addition in non-standard number systems","display_name":"Parallel algorithms for addition in non-standard number systems","publication_year":2014,"publication_date":"2014-02-01","ids":{"openalex":"https://openalex.org/W2091002049","doi":"https://doi.org/10.1109/ita.2014.6804265","mag":"2091002049"},"language":"en","primary_location":{"id":"doi:10.1109/ita.2014.6804265","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ita.2014.6804265","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 Information Theory and Applications Workshop (ITA)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113448170","display_name":"Christiane Frougny","orcid":null},"institutions":[{"id":"https://openalex.org/I4210094115","display_name":"Laboratoire d'Informatique Algorithmique: Fondements et Applications","ror":"https://ror.org/00pbqgm18","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210094115","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Christiane Frougny","raw_affiliation_strings":["LIAFA, UMR 7089 CNRS and Universit\u00e9 Paris 7, Cedex, France","LIAFA, Univ. Paris 7, Paris, France"],"affiliations":[{"raw_affiliation_string":"LIAFA, UMR 7089 CNRS and Universit\u00e9 Paris 7, Cedex, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210094115","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIAFA, Univ. Paris 7, Paris, France","institution_ids":["https://openalex.org/I4210094115","https://openalex.org/I204730241"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065289831","display_name":"Pavel Heller","orcid":null},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Pavel Heller","raw_affiliation_strings":["Department of Mathematics, Czech Technical University in Prague, Czech Republic","Dept. of Math., Czech Tech. Univ. in Prague, Prague, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Czech Technical University in Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Dept. of Math., Czech Tech. Univ. in Prague, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053945124","display_name":"Edita Pelantov\u00e1","orcid":"https://orcid.org/0000-0003-3817-2943"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Edita Pelantova","raw_affiliation_strings":["Department of Mathematics, Czech Technical University in Prague, Czech Republic","Dept. of Math., Czech Tech. Univ. in Prague, Prague, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Czech Technical University in Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Dept. of Math., Czech Tech. Univ. in Prague, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027050564","display_name":"Milena Svobodov\u00e1","orcid":"https://orcid.org/0000-0003-0337-7922"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Milena Svobodova","raw_affiliation_strings":["Department of Mathematics, Czech Technical University in Prague, Czech Republic","Dept. of Math., Czech Tech. Univ. in Prague, Prague, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Czech Technical University in Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Dept. of Math., Czech Tech. Univ. in Prague, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5113448170"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210094115"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13915119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9976000189781189,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9976000189781189,"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":0.9933000206947327,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6141255497932434},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.6018702983856201},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5981276631355286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5901150107383728},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.589152991771698},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.577178418636322},{"id":"https://openalex.org/keywords/division-algorithm","display_name":"Division algorithm","score":0.5583117008209229},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.5455188751220703},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5307700037956238},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4837946593761444},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4828389286994934},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.43645691871643066},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.43374723196029663},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4006073772907257},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3767581582069397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3444064259529114},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16941583156585693}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6141255497932434},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.6018702983856201},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5981276631355286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5901150107383728},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.589152991771698},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.577178418636322},{"id":"https://openalex.org/C190715199","wikidata":"https://www.wikidata.org/wiki/Q3526714","display_name":"Division algorithm","level":3,"score":0.5583117008209229},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.5455188751220703},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5307700037956238},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4837946593761444},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4828389286994934},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.43645691871643066},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.43374723196029663},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4006073772907257},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3767581582069397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3444064259529114},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16941583156585693},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ita.2014.6804265","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ita.2014.6804265","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 Information Theory and Applications Workshop (ITA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309972","display_name":"\u010cesk\u00e9 Vysok\u00e9 U\u010den\u00ed Technick\u00e9 v Praze","ror":"https://ror.org/03kqpb082"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W113031818","https://openalex.org/W1496427046","https://openalex.org/W1548974324","https://openalex.org/W1586417893","https://openalex.org/W1644429597","https://openalex.org/W1967808703","https://openalex.org/W1981034639","https://openalex.org/W2015700892","https://openalex.org/W2024581566","https://openalex.org/W2039564609","https://openalex.org/W2075595154","https://openalex.org/W2089164015","https://openalex.org/W2123320610","https://openalex.org/W2131256658","https://openalex.org/W2152310641","https://openalex.org/W2160949125","https://openalex.org/W2187226754","https://openalex.org/W2487890947","https://openalex.org/W2559887101","https://openalex.org/W2916844179","https://openalex.org/W6687306805"],"related_works":["https://openalex.org/W2038759377","https://openalex.org/W3093500249","https://openalex.org/W3094080891","https://openalex.org/W2886205627","https://openalex.org/W1601569507","https://openalex.org/W1559374008","https://openalex.org/W4389142747","https://openalex.org/W2243249360","https://openalex.org/W2064782566","https://openalex.org/W2171048434"],"abstract_inverted_index":{"In":[0,40,54],"1961":[1],"Avizienis":[2],"proposed":[3],"a":[4,65,80,90],"parallel":[5,43,91,122,128],"algorithm":[6,24,92],"for":[7,47],"addition":[8,26,44,86],"in":[9,27],"base":[10,63],"10":[11],"with":[12,102],"digit":[13,118],"set":[14,81,119],"A":[15],"=":[16],"{-6,":[17],"-5,":[18],"...,":[19],"5,":[20],"6}.":[21],"Such":[22],"an":[23,99],"performs":[25],"constant":[28],"time,":[29],"independently":[30],"of":[31,34,37,82,105,113,116],"the":[32,35,38,62,111,114,117],"length":[33],"representation":[36],"summands.":[39],"computer":[41],"arithmetic":[42],"is":[45,64,87,98],"used":[46],"speeding":[48],"up":[49],"multiplication":[50],"and":[51,94],"division":[52],"algorithms.":[53],"this":[55],"work":[56],"we":[57,77],"consider":[58],"number":[59,67,101],"systems":[60],"where":[61],"complex":[66],"\u03b2":[68,97],"such":[69],"that":[70,76,120],"|\u03b2|":[71],">":[72],"1.":[73,107],"We":[74,108,124],"show":[75],"can":[78],"find":[79],"signed-digits":[83],"on":[84],"which":[85],"realizable":[88],"by":[89],"if":[93,96],"only":[95],"algebraic":[100],"no":[103],"conjugate":[104],"modulus":[106],"then":[109],"address":[110],"question":[112],"size":[115],"permits":[121],"addition.":[123,129],"also":[125],"investigate":[126],"block":[127]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
