{"id":"https://openalex.org/W1972026679","doi":"https://doi.org/10.2307/2271779","title":"\u201cHelping\u201d: several formalizations","display_name":"\u201cHelping\u201d: several formalizations","publication_year":1975,"publication_date":"1975-12-01","ids":{"openalex":"https://openalex.org/W1972026679","doi":"https://doi.org/10.2307/2271779","mag":"1972026679"},"language":"en","primary_location":{"id":"doi:10.2307/2271779","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271779","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5071944803","display_name":"Nancy Lynch","orcid":"https://orcid.org/0000-0003-3045-265X"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nancy Lynch","raw_affiliation_strings":["University of Southern California, los Angeles, California90007","University of Southern California, Los Angeles, California;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Southern California, los Angeles, California90007","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"University of Southern California, Los Angeles, California;","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071944803"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.5971,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.82437811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"40","issue":"4","first_page":"555","last_page":"566"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9994999766349792,"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/T11567","display_name":"semigroups and automata theory","score":0.9994999766349792,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9994000196456909,"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/turing-machine","display_name":"Turing machine","score":0.7211822271347046},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.576339602470398},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5736867785453796},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.5305718779563904},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5300096273422241},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48138192296028137},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4581311345100403},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.43614262342453003},{"id":"https://openalex.org/keywords/non-deterministic-turing-machine","display_name":"Non-deterministic Turing machine","score":0.4335731863975525},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41167688369750977},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.38736188411712646},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.3426278233528137},{"id":"https://openalex.org/keywords/universal-turing-machine","display_name":"Universal Turing machine","score":0.29586073756217957},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22599411010742188}],"concepts":[{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.7211822271347046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.576339602470398},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5736867785453796},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.5305718779563904},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5300096273422241},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48138192296028137},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4581311345100403},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.43614262342453003},{"id":"https://openalex.org/C15190523","wikidata":"https://www.wikidata.org/wiki/Q1190223","display_name":"Non-deterministic Turing machine","level":5,"score":0.4335731863975525},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41167688369750977},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.38736188411712646},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3426278233528137},{"id":"https://openalex.org/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.29586073756217957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22599411010742188},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2271779","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271779","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183739577","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739577","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1508780728","https://openalex.org/W1981455469","https://openalex.org/W2007464118","https://openalex.org/W2020242021","https://openalex.org/W2036265926","https://openalex.org/W2066356146","https://openalex.org/W2089442854","https://openalex.org/W2167636857","https://openalex.org/W2401610261","https://openalex.org/W2530006810","https://openalex.org/W2532450662","https://openalex.org/W2905135108","https://openalex.org/W2971268466"],"related_works":["https://openalex.org/W2146459129","https://openalex.org/W2950065312","https://openalex.org/W4388215614","https://openalex.org/W2925112333","https://openalex.org/W3190027049","https://openalex.org/W2013091420","https://openalex.org/W2134140745","https://openalex.org/W1555195996","https://openalex.org/W3037086320","https://openalex.org/W21360042"],"abstract_inverted_index":{"Much":[0],"recent":[1],"work":[2],"in":[3,108,145,157,253,263],"the":[4,25,37,46,69,73,76,85,125,154,158,167,171,174,177,209,288,298],"theory":[5],"of":[6,18,30,48,75,88,100,105,153,173,188,208,211,234,242,276,282,290,300],"computational":[7],"complexity":[8,277,289],"([Me],":[9],"[FR].":[10],"[SI])":[11],"is":[12,137,162,268],"concerned":[13],"with":[14,134,214],"establishing":[15],"\u201cthe":[16],"complexity\u201d":[17],"various":[19],"recursive":[20],"functions,":[21],"as":[22,98],"measured":[23],"by":[24],"time":[26,111,126],"or":[27,103],"space":[28,224,254],"requirements":[29],"Turing":[31,121,222],"machines":[32],"which":[33,216,245,284],"compute":[34,57],"them.":[35],"In":[36],"above":[38],"work,":[39],"we":[40,81,148,246],"also":[41,237],"observe":[42],"another":[43],"phenomenon:":[44],"knowing":[45],"values":[47],"certain":[49,52,204],"functions":[50,54,71],"makes":[51],"other":[53,77,258],"easier":[55],"to":[56,113,115,128,142,164,176,219,280],"than":[58],"they":[59],"would":[60],"be":[61,116,140,183,251],"without":[62],"this":[63,240],"knowledge.":[64],"We":[65,236],"could":[66],"say":[67,165],"that":[68,84,166,239,266,281],"auxiliary":[70],"\u201chelp\u201d":[72,297],"computation":[74,172,299],"functions.":[78],"For":[79],"example,":[80],"may":[82,182,249],"conjecture":[83],"\u201cpolynomial-complete\u201d":[86],"problems":[87],"Cook":[89],"[C]":[90],"and":[91,94,196],"Karp":[92],"[K]":[93],"Stockmeyer":[95,197],"[S2],":[96],"such":[97],"satisfiability":[99,168],"propositional":[101,159],"formulas":[102,156],"3-colorability":[104],"planar":[106,132],"graphs,":[107],"fact":[109],"require":[110],"proportional":[112],"nlog2n":[114],"computed":[117],"on":[118,230],"a":[119,131,143,150,192,203],"deterministic":[120],"machine.":[122],"Then":[123],"since":[124],"required":[127],"decide":[129],"if":[130,147],"graph":[133],"n":[135,146],"nodes":[136],"3-colorable":[138],"can":[139],"lowered":[141],"polynomial":[144],"have":[149,199],"precomputed":[151],"table":[152],"satisfiable":[155],"calculus,":[160],"it":[161],"natural":[163],"problem":[169,270],"\u201chelps\u201d":[170],"answers":[175],"3-coloring":[178],"problem.":[179],"Similar":[180],"remarks":[181],"made":[184],"for":[185,202,226,256],"any":[186],"pair":[187],"polynomial-complete":[189],"problems.":[190],"As":[191],"further":[193],"illustration,":[194],"Meyer":[195],"[MS]":[198],"shown":[200],"that,":[201],"alphabet":[205],"\u03a3,":[206],"recognition":[207],"set":[210,233,241],"regular":[212,243],"expressions":[213],"squaring":[215],"are":[217],"equivalent":[218],"\u03a3*":[220],"requires":[221],"machine":[223],"cn":[225],"some":[227,257,269],"constant":[228,259],"c,":[229],"an":[231,273],"infinite":[232],"arguments.":[235],"know":[238],"expressions,":[244],"call":[247],"RSQ,":[248,283],"actually":[250],"recognized":[252],"dn":[255],"d.":[260],"Theorem":[261],"6.2":[262],"[LMF]":[264],"implies":[265],"there":[267],"(not":[271],"necessarily":[272],"interesting":[274],"one)":[275],"approximately":[278],"equal":[279],"does":[285,295],"not":[286,296],"reduce":[287],"RSQ":[291],"below":[292],"cn.":[293],"It":[294],"RSQ.":[301]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}