{"id":"https://openalex.org/W7100795383","doi":null,"title":"2.2 Basic Idea of G\u00f6del Machine............................ 4","display_name":"2.2 Basic Idea of G\u00f6del Machine............................ 4","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W7100795383"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.5205","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.5205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0309048v4.pdf","raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"J\u00fcrgen Schmidhuber","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J\u00fcrgen Schmidhuber","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9794999957084656,"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":0.9794999957084656,"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":0.00800000037997961,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.003700000001117587,"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/global-optimality","display_name":"global optimality","score":0.6190000176429749},{"id":"https://openalex.org/keywords/utility-functions","display_name":"utility functions","score":0.5270000100135803}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7551000118255615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6327000260353088},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5720999836921692},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5641999840736389},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5027999877929688},{"id":"https://openalex.org/C3019612716","wikidata":"https://www.wikidata.org/wiki/Q730920","display_name":"Problem solver","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.3935999870300293},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.3720000088214874},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.3718000054359436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3677999973297119},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3427000045776367},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.3244999945163727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2996000051498413},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.2856999933719635},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2833999991416931},{"id":"https://openalex.org/C19754495","wikidata":"https://www.wikidata.org/wiki/Q3435924","display_name":"Computational problem","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.5205","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.5205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0309048v4.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W158468099","https://openalex.org/W2155277832","https://openalex.org/W6902784969","https://openalex.org/W1626249333","https://openalex.org/W2101684037","https://openalex.org/W186126576","https://openalex.org/W2033006747","https://openalex.org/W7221439410","https://openalex.org/W2062016088","https://openalex.org/W96894755"],"abstract_inverted_index":{"We":[0,101],"present":[1],"the":[2,44,49,54,57,76,112,125,157,160],"first":[3,114],"class":[4],"of":[5,31,75,147,162],"mathematically":[6],"rigorous,":[7],"general,":[8],"fully":[9],"self-referential,":[10],"selfimproving,":[11],"optimally":[12,151],"efficient":[13],"problem":[14,26],"solvers.":[15],"Inspired":[16],"by":[17,63,156],"Kurt":[18],"G\u00f6del\u2019s":[19],"celebrated":[20],"selfreferential":[21],"formulas":[22],"(1931),":[23],"such":[24,104,163],"a":[25,41,96,105],"solver":[27],"rewrites":[28],"any":[29,153],"part":[30,74],"its":[32],"own":[33],"code":[34,60,113],"as":[35,37],"soon":[36],"it":[38,94,119],"has":[39],"found":[40],"proof":[42,69,86,126,138],"that":[43,103,118],"rewrite":[45],"is":[46,72,107,120,165],"useful,":[47,98],"where":[48],"problem-dependent":[50],"utility":[51,161],"function":[52],"and":[53,56,82],"hardware":[55],"entire":[58],"initial":[59,68,77],"are":[61,91],"described":[62],"axioms":[64],"encoded":[65],"in":[66],"an":[67,144],"searcher":[70,80],"which":[71],"also":[73],"code.":[78],"The":[79],"systematically":[81],"efficiently":[83],"tests":[84],"computable":[85,99],"techniques":[87],"(programs":[88],"whose":[89],"outputs":[90],"proofs)":[92],"until":[93],"finds":[95],"provably":[97],"self-rewrite.":[100],"show":[102],"self-rewrite":[106],"globally":[108],"optimal\u2014no":[109],"local":[110],"maxima!\u2014since":[111],"had":[115],"to":[116,123],"prove":[117],"not":[121,141],"useful":[122],"continue":[124],"search":[127],"for":[128],"alternative":[129],"self-rewrites.":[130],"Unlike":[131],"previous":[132],"non-self-referential":[133],"methods":[134],"based":[135],"on":[136],"hardwired":[137],"searchers,":[139],"ours":[140],"only":[142],"boasts":[143],"optimal":[145],"order":[146],"complexity":[148],"but":[149],"can":[150],"reduce":[152],"slowdowns":[154],"hidden":[155],"O()-notation,":[158],"provided":[159],"speed-ups":[164],"provable":[166]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-27T00:00:00"}