{"id":"https://openalex.org/W2924313066","doi":"https://doi.org/10.1109/tc.2019.2906201","title":"Boolean Minimization of Projected Sums of Products via Boolean Relations","display_name":"Boolean Minimization of Projected Sums of Products via Boolean Relations","publication_year":2019,"publication_date":"2019-03-19","ids":{"openalex":"https://openalex.org/W2924313066","doi":"https://doi.org/10.1109/tc.2019.2906201","mag":"2924313066"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2019.2906201","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2019.2906201","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2434/644845","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032558381","display_name":"Anna Bernasconi","orcid":"https://orcid.org/0000-0003-0263-5221"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Anna Bernasconi","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 di Pisa, Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0263-5221","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076933640","display_name":"Valentina Ciriani","orcid":"https://orcid.org/0000-0002-0469-4201"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Valentina Ciriani","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0002-0469-4201","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milano, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047355764","display_name":"Gabriella Trucco","orcid":"https://orcid.org/0000-0002-5904-0969"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gabriella Trucco","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0002-5904-0969","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milano, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084281460","display_name":"Tiziano Villa","orcid":"https://orcid.org/0000-0002-9671-8804"},"institutions":[{"id":"https://openalex.org/I119439378","display_name":"University of Verona","ror":"https://ror.org/039bp8j42","country_code":"IT","type":"education","lineage":["https://openalex.org/I119439378"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Tiziano Villa","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 di Verona, Verona, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9671-8804","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 di Verona, Verona, Italy","institution_ids":["https://openalex.org/I119439378"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5784,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68549153,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"68","issue":"9","first_page":"1269","last_page":"1282"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9939000010490417,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9907000064849854,"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/boolean-function","display_name":"Boolean function","score":0.8124273419380188},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.7766309976577759},{"id":"https://openalex.org/keywords/product-term","display_name":"Product term","score":0.7424685955047607},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.719796359539032},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6269375085830688},{"id":"https://openalex.org/keywords/circuit-minimization-for-boolean-functions","display_name":"Circuit minimization for Boolean functions","score":0.6120182275772095},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.577592134475708},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.5366657972335815},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4991939067840576},{"id":"https://openalex.org/keywords/implicant","display_name":"Implicant","score":0.475896954536438},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47456198930740356},{"id":"https://openalex.org/keywords/and-inverter-graph","display_name":"And-inverter graph","score":0.47241392731666565},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4698958098888397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4358215630054474},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41953739523887634},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4178916811943054},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.41225606203079224},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3168199062347412},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.25484153628349304},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.23861342668533325},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22724485397338867},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09469392895698547}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.8124273419380188},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.7766309976577759},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.7424685955047607},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.719796359539032},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6269375085830688},{"id":"https://openalex.org/C94992772","wikidata":"https://www.wikidata.org/wiki/Q6667469","display_name":"Circuit minimization for Boolean functions","level":4,"score":0.6120182275772095},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.577592134475708},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.5366657972335815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4991939067840576},{"id":"https://openalex.org/C102487863","wikidata":"https://www.wikidata.org/wiki/Q1291626","display_name":"Implicant","level":4,"score":0.475896954536438},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47456198930740356},{"id":"https://openalex.org/C196836630","wikidata":"https://www.wikidata.org/wiki/Q4753279","display_name":"And-inverter graph","level":4,"score":0.47241392731666565},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4698958098888397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4358215630054474},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41953739523887634},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4178916811943054},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41225606203079224},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3168199062347412},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25484153628349304},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.23861342668533325},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22724485397338867},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09469392895698547},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tc.2019.2906201","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2019.2906201","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},{"id":"pmh:oai:air.unimi.it:2434/644845","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/644845","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arpi.unipi.it:11568/1051815","is_oa":true,"landing_page_url":"http://hdl.handle.net/11568/1051815","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arpi.unipi.it:11568/998652","is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/998652","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:air.unimi.it:2434/644845","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/644845","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W110753034","https://openalex.org/W1489746688","https://openalex.org/W1528837436","https://openalex.org/W1535358336","https://openalex.org/W1776822698","https://openalex.org/W2011342051","https://openalex.org/W2013021291","https://openalex.org/W2015589329","https://openalex.org/W2021985366","https://openalex.org/W2050487566","https://openalex.org/W2057473176","https://openalex.org/W2070242292","https://openalex.org/W2079738422","https://openalex.org/W2082448265","https://openalex.org/W2086342996","https://openalex.org/W2086526381","https://openalex.org/W2093675663","https://openalex.org/W2096365323","https://openalex.org/W2100465945","https://openalex.org/W2100921984","https://openalex.org/W2105761964","https://openalex.org/W2106576948","https://openalex.org/W2113408440","https://openalex.org/W2114381689","https://openalex.org/W2124618076","https://openalex.org/W2129030791","https://openalex.org/W2135652786","https://openalex.org/W2146660848","https://openalex.org/W2149693580","https://openalex.org/W2155858070","https://openalex.org/W2158292008","https://openalex.org/W2165643425","https://openalex.org/W2545400013","https://openalex.org/W2587513648","https://openalex.org/W2769903157","https://openalex.org/W2951543455","https://openalex.org/W3014182972","https://openalex.org/W3104446142","https://openalex.org/W3141394097","https://openalex.org/W4211064314","https://openalex.org/W4248978280","https://openalex.org/W4251019779","https://openalex.org/W6604585854","https://openalex.org/W6629199164","https://openalex.org/W6677110078","https://openalex.org/W6683165842"],"related_works":["https://openalex.org/W2234833091","https://openalex.org/W4231391991","https://openalex.org/W3003936732","https://openalex.org/W2516690985","https://openalex.org/W2077017336","https://openalex.org/W2368408282","https://openalex.org/W2063425181","https://openalex.org/W2062972911","https://openalex.org/W2105128170","https://openalex.org/W1762672179"],"abstract_inverted_index":{"Projected":[0],"Sums":[1],"of":[2,67,81,117,124,130,142],"Products":[3],"(PSOPs)":[4],"are":[5,84,104],"a":[6,15,24,28,32,40,109,114],"Generalized":[7],"Shannon":[8],"Decomposition":[9],"(GSD)":[10],"with":[11,74,108,150],"remainder":[12,107],"that":[13,50,59,77,103,112],"restructures":[14],"logic":[16,20,25],"function":[17],"into":[18],"three":[19],"blocks":[21],"corresponding":[22],"to":[23,63,70],"bi-decomposition":[26],"plus":[27],"reminder":[29],"generated":[30],"by":[31],"cofactoring":[33,125],"function.":[34],"In":[35],"this":[36],"paper":[37],"we":[38,99],"discuss":[39],"Boolean":[41,71,119,148],"synthesis":[42],"technique":[43,87],"for":[44,121,154],"PSOPs,":[45],"which":[46],"exploits":[47],"the":[48,51,65,75,82,92,101,106,118,128,138,143],"fact":[49],"resulting":[52],"logical":[53],"structure":[54],"induces":[55],"don't":[56],"care":[57],"conditions":[58],"can":[60],"be":[61],"exploited":[62],"reduce":[64],"problem":[66],"area":[68,141],"minimization":[69],"relation":[72,120],"minimization,":[73],"guarantee":[76],"all":[78],"valid":[79],"realizations":[80],"circuit":[83],"considered.":[85],"This":[86],"is":[88],"more":[89],"general":[90],"than":[91],"algebraic":[93],"methods":[94],"investigated":[95],"so":[96],"far.":[97],"Moreover,":[98],"characterize":[100],"points":[102],"in":[105,140],"simple":[110],"procedure":[111],"implies":[113],"fast":[115],"construction":[116],"important":[122],"classes":[123],"functions":[126],"like":[127],"chain":[129],"XORs":[131],"or":[132],"ANDs.":[133],"We":[134],"report":[135],"experiments":[136],"confirming":[137],"effectiveness":[139],"proposed":[144],"approach":[145],"based":[146],"on":[147],"relations,":[149],"better":[151],"run":[152],"times":[153],"some":[155],"cost":[156],"functions.":[157]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-04-01T00:00:00"}