{"id":"https://openalex.org/W2017266350","doi":"https://doi.org/10.1109/tc.1972.5009017","title":"Minimal Input-Memory and Output-Memory Finite-State Machines","display_name":"Minimal Input-Memory and Output-Memory Finite-State Machines","publication_year":1972,"publication_date":"1972-06-01","ids":{"openalex":"https://openalex.org/W2017266350","doi":"https://doi.org/10.1109/tc.1972.5009017","mag":"2017266350"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1972.5009017","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1972.5009017","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050336586","display_name":"K. Vairavan","orcid":null},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"K. Vairavan","raw_affiliation_strings":["Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201","Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201","institution_ids":["https://openalex.org/I43579087"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201.#TAB#","institution_ids":["https://openalex.org/I43579087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050336586"],"corresponding_institution_ids":["https://openalex.org/I43579087"],"apc_list":null,"apc_paid":null,"fwci":1.2618,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.78195212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"C-21","issue":"6","first_page":"598","last_page":"602"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38763532042503357},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3711913824081421},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35803431272506714}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38763532042503357},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3711913824081421},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35803431272506714}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1972.5009017","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1972.5009017","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1967683545","https://openalex.org/W2012588232","https://openalex.org/W2016258810","https://openalex.org/W2052053914","https://openalex.org/W2074158701","https://openalex.org/W2075703340","https://openalex.org/W2078098287","https://openalex.org/W2117260532"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857"],"abstract_inverted_index":{"A":[0],"finite-state":[1],"machine":[2],"(FSM)":[3],"is":[4,15,43,63],"said":[5],"to":[6,88],"have":[7],"finite":[8],"input-memory,":[9],"\u03bci(finite":[10],"output-memory":[11,109],"\u03bco)":[12],"if":[13],"\u03bci(\u03bco)":[14,33],"the":[16,64,77,115,119,122,129],"least":[17],"integer":[18,32],"such":[19,31],"that":[20,46,76],"yk=":[21],"f(Xk,":[22,26],"Xk-1,...,":[23],"Xk-\u03bci),":[24],"(yk=":[25],"yk-1,...,":[27],"yk-\u03bco)).":[28],"If":[29],"no":[30],"exists":[34],"then":[35],"by":[36,84],"convention":[37],"\u03bci=":[38,106],"\u221e":[39],"(\u03bc0=":[40],"\u221e).":[41],"It":[42],"well":[44],"known":[45],"for":[47,90],"a":[48,86,95],"nondegenerate":[49],"binary-input":[50,96],"binary-output":[51,97],"FSM":[52,98],"M,":[53],"\u03bci\u2265":[54],"[log2":[55,59],"n]":[56],"(\u03bco":[57],"\u2265":[58],"n]),":[60],"where":[61],"n":[62,92,100],"number":[65,130],"of":[66,117,121,131],"non-equivalent":[67],"states":[68,102],"in":[69],"M.":[70],"In":[71,114],"this":[72],"note":[73],"we":[74,127],"show":[75],"above":[78],"bound":[79,124],"cannot":[80],"be":[81],"improved":[82],"upon":[83],"giving":[85],"procedure":[87],"construct,":[89],"any":[91],">":[93],"0,":[94],"with":[99],"nonequivalent":[101],"and":[103],"minimal":[104,133],"input-memory":[105],"[log2n]":[107],"(minimal":[108],"\u03bco=":[110],"[":[111],"log2":[112],"n]).":[113],"process":[116],"proving":[118],"tightness":[120],"lower":[123],"on":[125],"\u03bci(\u03bco),":[126],"enumerate":[128],"distinct":[132],"binary":[134],"r-stage":[135],"feed-forward":[136],"(output":[137],"feedback)":[138],"shift":[139],"registers.":[140]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}