{"id":"https://openalex.org/W2167373933","doi":"https://doi.org/10.1109/tec.1961.5219224","title":"The Realization of Symmetric Switching Functions with Linear-Input Logical Elements","display_name":"The Realization of Symmetric Switching Functions with Linear-Input Logical Elements","publication_year":1961,"publication_date":"1961-09-01","ids":{"openalex":"https://openalex.org/W2167373933","doi":"https://doi.org/10.1109/tec.1961.5219224","mag":"2167373933"},"language":"en","primary_location":{"id":"doi:10.1109/tec.1961.5219224","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tec.1961.5219224","pdf_url":null,"source":{"id":"https://openalex.org/S60436882","display_name":"IEEE Transactions on Electronic Computers","issn_l":"0367-7508","issn":["0367-7508"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Electronic 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/A5089543844","display_name":"William H. Kautz","orcid":null},"institutions":[{"id":"https://openalex.org/I4210099336","display_name":"Menlo School","ror":"https://ror.org/01240pn49","country_code":"US","type":"education","lineage":["https://openalex.org/I4210099336"]},{"id":"https://openalex.org/I1298353152","display_name":"SRI International","ror":"https://ror.org/05s570m15","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1298353152"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"William H. Kautz","raw_affiliation_strings":["Stanford Research Institute, Menlo Park, CA, USA"],"affiliations":[{"raw_affiliation_string":"Stanford Research Institute, Menlo Park, CA, USA","institution_ids":["https://openalex.org/I1298353152","https://openalex.org/I4210099336"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089543844"],"corresponding_institution_ids":["https://openalex.org/I1298353152","https://openalex.org/I4210099336"],"apc_list":null,"apc_paid":null,"fwci":7.8045,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.97685632,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"EC-10","issue":"3","first_page":"371","last_page":"378"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9933000206947327,"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"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9933000206947327,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9909999966621399,"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9839000105857849,"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/realization","display_name":"Realization (probability)","score":0.7887501120567322},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.5435913801193237},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5197943449020386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5112922191619873},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4704500734806061},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.42789626121520996},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42484116554260254},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.4225695729255676},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3607892394065857},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34619414806365967},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23292779922485352},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07441645860671997}],"concepts":[{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.7887501120567322},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.5435913801193237},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5197943449020386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5112922191619873},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4704500734806061},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.42789626121520996},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42484116554260254},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.4225695729255676},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3607892394065857},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34619414806365967},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23292779922485352},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07441645860671997},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tec.1961.5219224","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tec.1961.5219224","pdf_url":null,"source":{"id":"https://openalex.org/S60436882","display_name":"IEEE Transactions on Electronic Computers","issn_l":"0367-7508","issn":["0367-7508"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Electronic Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323145","display_name":"Institute of Nuclear Energy Research","ror":"https://ror.org/052jx3443"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2053619330","https://openalex.org/W2103676795","https://openalex.org/W2119024968","https://openalex.org/W2169059873","https://openalex.org/W2319160178"],"related_works":["https://openalex.org/W2092886012","https://openalex.org/W2145874891","https://openalex.org/W2170281757","https://openalex.org/W2119028753","https://openalex.org/W2790802381","https://openalex.org/W2511750106","https://openalex.org/W1982026196","https://openalex.org/W3094037537","https://openalex.org/W3194134751","https://openalex.org/W2151933547"],"abstract_inverted_index":{"The":[0],"problem":[1],"of":[2,7,16,27,37,52,73,77],"synthesizing":[3],"switching":[4,18],"networks":[5,46],"out":[6],"linear-input":[8],"(threshold)":[9],"elements":[10,28],"is":[11,39,67],"studied":[12],"for":[13,24,48,60],"the":[14,25,70],"class":[15],"symmetric":[17,50],"functions.":[19],"Tight":[20],"bounds":[21],"are":[22],"derived":[23],"number":[26,75],"required":[29],"in":[30],"a":[31,35],"minimal":[32],"realization,":[33],"and":[34,59],"method":[36],"synthesis":[38],"presented":[40],"which":[41],"yields":[42],"economical":[43],"networks.":[44],"Minimal":[45],"result":[47],"all":[49],"functions":[51],"no":[53],"more":[54],"than":[55],"about":[56,83],"twelve":[57],"variables,":[58],"several":[61],"other":[62],"cases.":[63],"In":[64],"particular,":[65],"it":[66],"shown":[68],"how":[69],"parity":[71],"function":[72],"any":[74],"n":[76],"variables":[78],"can":[79],"be":[80],"realized":[81],"with":[82],"log2(n)":[84],"elements.":[85]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}