{"id":"https://openalex.org/W2133124702","doi":"https://doi.org/10.1007/s11047-014-9438-5","title":"Logic circuits from zero forcing","display_name":"Logic circuits from zero forcing","publication_year":2014,"publication_date":"2014-07-25","ids":{"openalex":"https://openalex.org/W2133124702","doi":"https://doi.org/10.1007/s11047-014-9438-5","mag":"2133124702","pmid":"https://pubmed.ncbi.nlm.nih.gov/26300713"},"language":"en","primary_location":{"id":"doi:10.1007/s11047-014-9438-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-014-9438-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-014-9438-5.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11047-014-9438-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Daniel Burgarth","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Daniel Burgarth","raw_affiliation_strings":["Department of Mathematics and Physics, Aberystwyth University, Aberystwyth, SY23 3BZ UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, Aberystwyth University, Aberystwyth, SY23 3BZ UK","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Vittorio Giovannetti","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vittorio Giovannetti","raw_affiliation_strings":["NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza dei Cavalieri 7, 56126 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza dei Cavalieri 7, 56126 Pisa, Italy","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Leslie Hogben","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leslie Hogben","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, IA 50011 USA ; American Institute of Mathematics, 360 Portage Ave, Palo Alto, CA 94306 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA 50011 USA ; American Institute of Mathematics, 360 Portage Ave, Palo Alto, CA 94306 USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Simone Severini","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simone Severini","raw_affiliation_strings":["Department of Computer Science, University College London, London, WC1E 6BT UK ; Department of Physics and Astronomy, University College London, London, WC1E 6BT UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University College London, London, WC1E 6BT UK ; Department of Physics and Astronomy, University College London, London, WC1E 6BT UK","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Michael Young","orcid":null},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Young","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, IA 50011 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA 50011 USA","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":1870,"currency":"EUR","value_usd":2016},"fwci":1.2687,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.85778857,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"3","first_page":"485","last_page":"490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.6348999738693237,"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"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.6348999738693237,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.04560000076889992,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.032099999487400055,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.569100022315979},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.5400000214576721},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5327000021934509},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.47679999470710754},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.43560001254081726},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4172999858856201},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.396699994802475},{"id":"https://openalex.org/keywords/quantum-logic","display_name":"Quantum logic","score":0.39309999346733093},{"id":"https://openalex.org/keywords/logic-gate","display_name":"Logic gate","score":0.383899986743927}],"concepts":[{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.569100022315979},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.5400000214576721},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5327000021934509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4871000051498413},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.47679999470710754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4471000134944916},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.396699994802475},{"id":"https://openalex.org/C169460222","wikidata":"https://www.wikidata.org/wiki/Q1206311","display_name":"Quantum logic","level":4,"score":0.39309999346733093},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C119770614","wikidata":"https://www.wikidata.org/wiki/Q5516347","display_name":"Gadget","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.3601999878883362},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.34209999442100525},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.3287999927997589},{"id":"https://openalex.org/C192061203","wikidata":"https://www.wikidata.org/wiki/Q765620","display_name":"Quantum Turing machine","level":5,"score":0.3190000057220459},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.29789999127388},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28690001368522644},{"id":"https://openalex.org/C94992772","wikidata":"https://www.wikidata.org/wiki/Q6667469","display_name":"Circuit minimization for Boolean functions","level":4,"score":0.2676999866962433},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.2639999985694885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2624000012874603},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.260699987411499},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s11047-014-9438-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-014-9438-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-014-9438-5.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},{"id":"pmid:26300713","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26300713","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural computing","raw_type":null},{"id":"pmh:oai:arXiv.org:1106.4403","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1106.4403","pdf_url":"https://arxiv.org/pdf/1106.4403","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:europepmc.org:3519511","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4541710","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:ricerca.sns.it:11384/73945","is_oa":true,"landing_page_url":"http://hdl.handle.net/11384/73945","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11047-014-9438-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-014-9438-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-014-9438-5.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4788835274","display_name":null,"funder_award_id":"EP/F043678/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320311090","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78"},{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320320283","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2133124702.pdf","grobid_xml":"https://content.openalex.org/works/W2133124702.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1996839950","https://openalex.org/W2012476164","https://openalex.org/W2019383400","https://openalex.org/W2055678622","https://openalex.org/W2066853877","https://openalex.org/W2108954600","https://openalex.org/W2110711640","https://openalex.org/W2114638353","https://openalex.org/W2147493617","https://openalex.org/W2175011670","https://openalex.org/W4242597152","https://openalex.org/W4251109627"],"related_works":[],"abstract_inverted_index":{"We":[0,27,51],"design":[1],"logic":[2],"circuits":[3,17,31],"based":[4],"on":[5,11],"the":[6,16,73,123,135,145,161],"notion":[7],"of":[8,15,56,62,75,125,137,139,163],"zero":[9,23,103,140,182],"forcing":[10,24,104,141,183],"graphs;":[12],"each":[13,44,63],"gate":[14],"is":[18,25,87,169,178],"a":[19,54,60,66,70,83,91,96,118,152,179],"gadget":[20],"in":[21,69,122,134,142,155,160],"which":[22,77],"performed.":[26],"show":[28,101],"that":[29,102],"such":[30],"can":[32,105],"evaluate":[33],"every":[34],"monotone":[35],"Boolean":[36,126,148],"function.":[37,64],"By":[38],"using":[39],"two":[40],"vertices":[41],"to":[42,109,131,174],"encode":[43],"logical":[45],"bit,":[46],"we":[47,100],"obtain":[48],"universal":[49],"computation.":[50,112],"also":[52,107],"highlight":[53],"phenomenon":[55,67],"\"back":[57],"forcing\"":[58],"as":[59],"property":[61],"Such":[65],"occurs":[68],"circuit":[71],"when":[72],"input":[74],"gates":[76],"have":[78],"been":[79],"already":[80],"used":[81,108],"at":[82,95],"given":[84],"time":[85],"step":[86],"further":[88],"modified":[89],"by":[90],"computation":[92,185],"actually":[93],"performed":[94],"later":[97],"stage.":[98],"Finally,":[99],"be":[106],"implement":[110],"reversible":[111],"The":[113],"model":[114],"introduced":[115],"here":[116],"provides":[117],"potentially":[119],"new":[120,153],"tool":[121],"analysis":[124],"functions,":[127],"with":[128,147,186],"particular":[129],"attention":[130],"monotonicity.":[132],"Moreover,":[133],"light":[136],"applications":[138],"quantum":[143,156,165],"mechanics,":[144],"link":[146,180],"functions":[149],"may":[150],"suggest":[151],"directions":[154],"control":[157],"theory":[158],"and":[159,184],"study":[162],"engineered":[164],"spin":[166],"systems.":[167],"It":[168],"an":[170],"open":[171],"technical":[172],"problem":[173],"verify":[175],"whether":[176],"there":[177],"between":[181],"contact":[187],"circuits.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-31T08:46:17.908082","created_date":"2016-06-24T00:00:00"}