{"id":"https://openalex.org/W4211231415","doi":"https://doi.org/10.3390/axioms11020066","title":"Logarithmic SAT Solution with Membrane Computing","display_name":"Logarithmic SAT Solution with Membrane Computing","publication_year":2022,"publication_date":"2022-02-08","ids":{"openalex":"https://openalex.org/W4211231415","doi":"https://doi.org/10.3390/axioms11020066"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11020066","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020066","pdf_url":"https://www.mdpi.com/2075-1680/11/2/66/pdf?version=1644993630","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/2/66/pdf?version=1644993630","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062330820","display_name":"Radu Nicolescu","orcid":"https://orcid.org/0000-0003-2498-1002"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Radu Nicolescu","raw_affiliation_strings":["School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083519582","display_name":"Michael J. Dinneen","orcid":"https://orcid.org/0000-0001-9977-525X"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Michael Dinneen","raw_affiliation_strings":["School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039841907","display_name":"James Cooper","orcid":"https://orcid.org/0000-0001-9954-3280"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"James Cooper","raw_affiliation_strings":["School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064053144","display_name":"Alec Henderson","orcid":"https://orcid.org/0000-0001-9233-5059"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Alec Henderson","raw_affiliation_strings":["School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062421721","display_name":"Yezhou Liu","orcid":"https://orcid.org/0000-0002-9296-7408"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Yezhou Liu","raw_affiliation_strings":["School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5062330820"],"corresponding_institution_ids":["https://openalex.org/I154130895"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0866,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.40154229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"2","first_page":"66","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10207","display_name":"Advanced biosensing and bioanalysis techniques","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9891999959945679,"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/logarithm","display_name":"Logarithm","score":0.7020738124847412},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.694812536239624},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.5577359199523926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5321817398071289},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.5088115334510803},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4959591329097748},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45161983370780945},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4361017942428589},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4206644296646118},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36984458565711975},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.360260009765625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05914008617401123}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7020738124847412},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.694812536239624},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.5577359199523926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5321817398071289},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.5088115334510803},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4959591329097748},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45161983370780945},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4361017942428589},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4206644296646118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36984458565711975},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.360260009765625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05914008617401123},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms11020066","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020066","pdf_url":"https://www.mdpi.com/2075-1680/11/2/66/pdf?version=1644993630","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:31012c16f48f489ebd8b4e740707e1c5","is_oa":true,"landing_page_url":"https://doaj.org/article/31012c16f48f489ebd8b4e740707e1c5","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 2, p 66 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/2/66/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11020066","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Axioms; Volume 11; Issue 2; Pages: 66","raw_type":"Text"},{"id":"pmh:oai:researchonline.jcu.edu.au:75510","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400519","display_name":"ResearchOnline at James Cook University (James Cook University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I86467917","host_organization_name":"James Cook University","host_organization_lineage":["https://openalex.org/I86467917"],"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":"Article"}],"best_oa_location":{"id":"doi:10.3390/axioms11020066","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020066","pdf_url":"https://www.mdpi.com/2075-1680/11/2/66/pdf?version=1644993630","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4211231415.pdf","grobid_xml":"https://content.openalex.org/works/W4211231415.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1607601471","https://openalex.org/W1690819463","https://openalex.org/W1984586189","https://openalex.org/W1995799881","https://openalex.org/W1996796733","https://openalex.org/W2022841964","https://openalex.org/W2034835975","https://openalex.org/W2078361986","https://openalex.org/W2156760067","https://openalex.org/W2158708642","https://openalex.org/W2313379588","https://openalex.org/W2532651643","https://openalex.org/W2917763030","https://openalex.org/W2943099128","https://openalex.org/W2996124030","https://openalex.org/W3104027319","https://openalex.org/W4246411629","https://openalex.org/W4251364654","https://openalex.org/W4254071110","https://openalex.org/W6637385950","https://openalex.org/W6649397586"],"related_works":["https://openalex.org/W3204703029","https://openalex.org/W1629505938","https://openalex.org/W1558483132","https://openalex.org/W2112173210","https://openalex.org/W1531835879","https://openalex.org/W207698748","https://openalex.org/W1969428672","https://openalex.org/W3005925191","https://openalex.org/W4221160330","https://openalex.org/W4211231415"],"abstract_inverted_index":{"P":[0,90],"systems":[1,19,130],"have":[2,20],"been":[3,21],"known":[4],"to":[5,13,23,30,121],"provide":[6,24],"efficient":[7,28],"polynomial":[8],"(often":[9],"linear)":[10],"deterministic":[11,85],"solutions":[12,29],"hard":[14],"problems.":[15],"In":[16],"particular,":[17],"cP":[18,96,129],"shown":[22],"very":[25],"crisp":[26],"and":[27,65,71,135],"such":[31],"problems,":[32],"which":[33,49],"are":[34],"typically":[35],"linear":[36],"with":[37],"small":[38,68],"coefficients.":[39],"Building":[40],"on":[41],"a":[42,67,100,106,109],"recent":[43],"result":[44,124],"by":[45,125],"Henderson":[46,126],"et":[47,127],"al.,":[48,128],"solves":[50],"SAT":[51],"in":[52,62,140],"square-root-sublinear":[53],"time,":[54,64],"this":[55,81],"paper":[56],"proposes":[57],"an":[58],"orders-of-magnitude-faster":[59],"solution,":[60],"running":[61],"logarithmic":[63,141],"using":[66],"fixed-sized":[69],"alphabet":[70],"ruleset":[72],"(25":[73],"rules).":[74],"To":[75],"the":[76,83],"best":[77],"of":[78,108],"our":[79],"knowledge,":[80],"is":[82,99,104],"fastest":[84],"solution":[86,102],"across":[87],"all":[88,94],"extant":[89],"system":[91],"variants.":[92],"Like":[93],"other":[95,137],"solutions,":[97],"it":[98],"complete":[101],"that":[103],"not":[105,115],"member":[107],"uniform":[110],"family":[111],"(and":[112],"thus":[113],"does":[114],"require":[116],"any":[117],"preprocessing).":[118],"Consequently,":[119],"according":[120],"another":[122],"reduction":[123],"can":[131],"also":[132],"solve":[133],"k-colouring":[134],"several":[136],"NP-complete":[138],"problems":[139],"time.":[142]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2022-02-13T00:00:00"}