{"id":"https://openalex.org/W2040704463","doi":"https://doi.org/10.1142/s0218126696000194","title":"TRANSFORMATION OF NESTED LOOPS INTO UNIFORM RECURRENCES AND THEIR MAPPING TO REGULAR PROCESSOR ARRAYS","display_name":"TRANSFORMATION OF NESTED LOOPS INTO UNIFORM RECURRENCES AND THEIR MAPPING TO REGULAR PROCESSOR ARRAYS","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W2040704463","doi":"https://doi.org/10.1142/s0218126696000194","mag":"2040704463"},"language":"en","primary_location":{"id":"doi:10.1142/s0218126696000194","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218126696000194","pdf_url":null,"source":{"id":"https://openalex.org/S167602672","display_name":"Journal of Circuits Systems and Computers","issn_l":"0218-1266","issn":["0218-1266","1793-6454"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Circuits, Systems and Computers","raw_type":"journal-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/A5058522486","display_name":"E.D. Kyriakis-Bitzaros","orcid":"https://orcid.org/0000-0002-4497-6158"},"institutions":[{"id":"https://openalex.org/I203474044","display_name":"National Centre of Scientific Research \"Demokritos\"","ror":"https://ror.org/038jp4m40","country_code":"GR","type":"facility","lineage":["https://openalex.org/I203474044"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"E.D. KYRIAKIS-BITZAROS","raw_affiliation_strings":["Institute of Microelectronics, NCSR \u201cDemokritos\u201d 15310 Agia Paraskevi, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Microelectronics, NCSR \u201cDemokritos\u201d 15310 Agia Paraskevi, Greece","institution_ids":["https://openalex.org/I203474044"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043131021","display_name":"Dimitrios Soudris","orcid":"https://orcid.org/0000-0002-6930-6847"},"institutions":[{"id":"https://openalex.org/I147962203","display_name":"Democritus University of Thrace","ror":"https://ror.org/03bfqnx40","country_code":"GR","type":"education","lineage":["https://openalex.org/I147962203"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"D.J. SOUDRIS","raw_affiliation_strings":["Laboratory of Electrical and Electronic Material Technology, Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, 67100, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Electrical and Electronic Material Technology, Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, 67100, Greece","institution_ids":["https://openalex.org/I147962203"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112615786","display_name":"C.E. Goutis","orcid":null},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"C.E. GOUTIS","raw_affiliation_strings":["VLSI Design Laboratory, Department of Electrical Engineering, University of Patras, 26100, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"VLSI Design Laboratory, Department of Electrical Engineering, University of Patras, 26100, Greece","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16717653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"06","issue":"03","first_page":"243","last_page":"265"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9645000100135803,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9645000100135803,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9581999778747559,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9571999907493591,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nested-loop-join","display_name":"Nested loop join","score":0.7515966892242432},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.6132989525794983},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5703687071800232},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5129165649414062},{"id":"https://openalex.org/keywords/processor-array","display_name":"Processor array","score":0.511742115020752},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4958573281764984},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4772343933582306},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4757615923881531},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.45352253317832947},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.44170430302619934},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4315444231033325},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4158661961555481},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15312409400939941},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.12806236743927002}],"concepts":[{"id":"https://openalex.org/C1306188","wikidata":"https://www.wikidata.org/wiki/Q4060687","display_name":"Nested loop join","level":2,"score":0.7515966892242432},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.6132989525794983},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5703687071800232},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5129165649414062},{"id":"https://openalex.org/C2776189500","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Processor array","level":2,"score":0.511742115020752},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4958573281764984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4772343933582306},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4757615923881531},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.45352253317832947},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.44170430302619934},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4315444231033325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4158661961555481},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15312409400939941},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.12806236743927002},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218126696000194","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218126696000194","pdf_url":null,"source":{"id":"https://openalex.org/S167602672","display_name":"Journal of Circuits Systems and Computers","issn_l":"0218-1266","issn":["0218-1266","1793-6454"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Circuits, Systems and Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2141424423","https://openalex.org/W2080027614","https://openalex.org/W115059224","https://openalex.org/W2099216186","https://openalex.org/W1596694782","https://openalex.org/W2344398102","https://openalex.org/W1970008223","https://openalex.org/W2159360349","https://openalex.org/W1985440756","https://openalex.org/W2040704463"],"abstract_inverted_index":{"A":[0],"methodology":[1,173],"for":[2],"transforming":[3],"a":[4,43,67,84],"class":[5],"of":[6,32,35,45,66,69,86,90,97,104,115,131,139,142,154,179],"iterative":[7],"algorithms,":[8],"expressed":[9],"in":[10,165],"nested":[11,38],"loops,":[12],"into":[13,22,83,101],"Uniform":[14],"Recurrent":[15],"Equation":[16],"(URE)":[17],"forms":[18],"and":[19,120],"their":[20,50],"mapping":[21,89],"regular":[23],"processor":[24,126,144,167,181],"array":[25,127,145,168],"architectures":[26,148],"is":[27,40,60,93,174],"presented.":[28],"The":[29,53,88,112,129,171],"propagation":[30],"space":[31,100],"the":[33,36,57,64,80,91,98,108,116,125,132,140,143,155,166,177,184],"variables":[34],"original":[37],"loop":[39],"specified":[41],"by":[42,49,63,95,150,176],"system":[44],"linear":[46,152],"equations":[47],"formed":[48],"index":[51,58,99,157],"functions.":[52],"data":[54],"flow":[55],"within":[56],"space,":[59],"then":[61],"localized":[62],"derivation":[65],"set":[68,85],"parametric":[70],"dependence":[71,110,113],"vectors,":[72],"which":[73],"eventually":[74],"can":[75],"be":[76],"used":[77],"to":[78,136,147],"transform":[79],"initial":[81],"algorithm":[82],"UREs.":[87],"UREs":[92],"accomplished":[94],"decomposition":[96],"independent":[102,133],"subsets":[103,117,134],"variable":[105],"instances":[106],"using":[107,151],"derived":[109,149],"vectors.":[111],"graphs":[114],"are":[118,122,169],"normalized":[119],"subsequently,":[121],"mapped":[123],"on":[124],"architecture.":[128],"exploitation":[130],"leads":[135],"significant":[137],"improvement":[138],"efficiency":[141],"compared":[146],"transformations":[153],"entire":[156],"space.":[158],"Under":[159],"certain":[160],"conditions,":[161],"only":[162],"local":[163],"interconnections":[164],"required.":[170],"proposed":[172],"illustrated":[175],"design":[178],"alternative":[180],"arrays":[182],"implementing":[183],"convolution":[185],"algorithm.":[186]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}