{"id":"https://openalex.org/W1869113160","doi":"https://doi.org/10.1109/lics.2002.1029842","title":"Calibrating computational feasibility by abstraction rank","display_name":"Calibrating computational feasibility by abstraction rank","publication_year":2003,"publication_date":"2003-06-25","ids":{"openalex":"https://openalex.org/W1869113160","doi":"https://doi.org/10.1109/lics.2002.1029842","mag":"1869113160"},"language":"en","primary_location":{"id":"doi:10.1109/lics.2002.1029842","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2002.1029842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 17th Annual IEEE Symposium on Logic in Computer Science","raw_type":"proceedings-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/A5018841823","display_name":"Dani\u00ebl Leivant","orcid":"https://orcid.org/0000-0003-4041-4382"},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Leivant","raw_affiliation_strings":["Computer Science Department, Indiana University, Bloomington, IN, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Indiana University, Bloomington, IN, USA","institution_ids":["https://openalex.org/I4210119109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018841823"],"corresponding_institution_ids":["https://openalex.org/I4210119109"],"apc_list":null,"apc_paid":null,"fwci":0.3545,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.56806459,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"345","last_page":"354"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9976999759674072,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5917732119560242},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.556814968585968},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5558220744132996},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.47037118673324585},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45200249552726746},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.43603450059890747},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38539591431617737},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33816272020339966},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16452378034591675}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5917732119560242},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.556814968585968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5558220744132996},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.47037118673324585},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45200249552726746},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.43603450059890747},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38539591431617737},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33816272020339966},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16452378034591675},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lics.2002.1029842","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2002.1029842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 17th Annual IEEE Symposium on Logic in Computer Science","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W17974129","https://openalex.org/W144522662","https://openalex.org/W659508351","https://openalex.org/W1489750944","https://openalex.org/W1493890316","https://openalex.org/W1503860275","https://openalex.org/W1525064220","https://openalex.org/W1534957303","https://openalex.org/W1553276022","https://openalex.org/W1571279515","https://openalex.org/W1581416890","https://openalex.org/W1654208522","https://openalex.org/W1981324778","https://openalex.org/W2039746135","https://openalex.org/W2041616904","https://openalex.org/W2049352524","https://openalex.org/W2149062436","https://openalex.org/W2211325406","https://openalex.org/W2914762105","https://openalex.org/W6600713429","https://openalex.org/W6629154057","https://openalex.org/W6758845221","https://openalex.org/W7048286187"],"related_works":["https://openalex.org/W2951695430","https://openalex.org/W4300891849","https://openalex.org/W2318687609","https://openalex.org/W91590591","https://openalex.org/W1525257472","https://openalex.org/W159772521","https://openalex.org/W2950100995","https://openalex.org/W3170064006","https://openalex.org/W2281582664","https://openalex.org/W2554039769"],"abstract_inverted_index":{"We":[0,89],"characterize":[1],"computationally":[2],"the":[3,37,61,143,153,175],"functions":[4,43,62,147,176],"provable":[5,48],"in":[6,64,104,112,121,142,152,178,190],"second":[7,106],"order":[8,19,107],"logic":[9],"with":[10,136],"set":[11,50],"existence":[12,51],"restricted":[13],"to":[14],"natural":[15,31,94],"classes":[16,35],"of":[17,23,33,39,54,162,164,169],"first":[18],"formulas.":[20],"A":[21],"classification":[22],"first-order":[24,167],"set-existence":[25,82],"by":[26],"implicational":[27,55],"rank":[28,56,170],"yields":[29,86],"a":[30,122,128,134,160],"hierarchy":[32],"complexity":[34],"within":[36],"class":[38],"Kalmar-elementary":[40],"functions:":[41],"The":[42,146,184],"over":[44,148,159],"{0,":[45,149],"1}*":[46,150],"constructively":[47],"using":[49,166],"for":[52,83,96],"formulas":[53,85],"/spl":[57,171],"les/k":[58],"are":[59,101,173],"precisely":[60,174],"computable":[63,177],"deterministic":[65,179],"time":[66,180],"O(exp/sub":[67,181],"k/(n)),":[68],"where":[69],"exp/sub":[70,76],"0/=U/sub":[71],"k/(/spl":[72],"lambda/n.n/sup":[73],"k/),":[74],"and":[75,93,109,111,116,124],"k+1/=2(exp/sub":[77],"k/)./sup":[78],"1/":[79],"In":[80],"particular,":[81],"positive":[84],"exactly":[87],"PTime.":[88],"thus":[90],"obtain":[91,133],"lean":[92],"formalisms":[95],"codifying":[97],"feasible":[98],"mathematics,":[99],"which":[100,139],"expressive":[102],"both":[103],"allowing":[105],"definitions":[108],"reasoning,":[110],"incorporating":[113],"equational":[114],"programming":[115],"reasoning":[117],"about":[118],"program":[119],"convergence":[120],"direct":[123],"uncoded":[125],"style.":[126],"Through":[127],"formula-as-type":[129],"morphism,":[130],"we":[131,140],"also":[132],"link":[135],"lambda":[137,155],"definability,":[138],"exhibit":[141],"full":[144],"paper:":[145],"definable":[151],"polymorphic":[154],"calculus":[156],"F/sub":[157],"2/":[158,183],"base":[161],"type":[163],"words,":[165],"type-arguments":[168],"les/k,":[172],"k/(n))./sup":[182],"poly-time":[185],"case":[186],"was":[187],"proved":[188],"(directly)":[189],"[15].":[191]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
