{"id":"https://openalex.org/W7203680732","doi":"https://doi.org/10.48550/arxiv.2608.16438","title":"The Value of a Prompt: An LLM-Relative Kolmogorov-Complexity Approach","display_name":"The Value of a Prompt: An LLM-Relative Kolmogorov-Complexity Approach","publication_year":2026,"publication_date":"2026-08-17","ids":{"openalex":"https://openalex.org/W7203680732","doi":"https://doi.org/10.48550/arxiv.2608.16438"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.16438","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16438","pdf_url":"https://arxiv.org/pdf/2608.16438","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.16438","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081609749","display_name":"Rafael Pass","orcid":"https://orcid.org/0000-0001-7440-5690","observed_orcids":["https://orcid.org/0000-0001-7440-5690"]},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]},{"id":"https://openalex.org/I4405261073","display_name":"Cornell Tech","ror":"https://ror.org/04qscbg47","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295","https://openalex.org/I4405261073"]}],"countries":["IL","US"],"is_corresponding":true,"raw_author_name":"Pass, Rafael","raw_affiliation_strings":["Cornell Tech , Technion , TAU"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell Tech , Technion , TAU","institution_ids":["https://openalex.org/I174306211","https://openalex.org/I4405261073"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081609749"],"corresponding_institution_ids":["https://openalex.org/I174306211","https://openalex.org/I4405261073"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9984999895095825,"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":0.9984999895095825,"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/T13904","display_name":"Artificial Intelligence Applications","score":9.999999747378752e-05,"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/T13898","display_name":"Diverse Interdisciplinary Research Studies","score":9.999999747378752e-05,"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/large-language-models","display_name":"large language models","score":0.7250000238418579},{"id":"https://openalex.org/keywords/token-cost","display_name":"token cost","score":0.375},{"id":"https://openalex.org/keywords/sampling-probability","display_name":"sampling probability","score":0.37599998712539673}],"concepts":[{"id":"https://openalex.org/C132010649","wikidata":"https://www.wikidata.org/wiki/Q189222","display_name":"Intuition","level":2,"score":0.6410999894142151},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5546000003814697},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5414999723434448},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5130000114440918},{"id":"https://openalex.org/C2779010991","wikidata":"https://www.wikidata.org/wiki/Q2720909","display_name":"Artifact (error)","level":2,"score":0.46709999442100525},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.4499000012874603},{"id":"https://openalex.org/C92424840","wikidata":"https://www.wikidata.org/wiki/Q7912772","display_name":"Value of information","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3732999861240387},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.3709999918937683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3508000075817108},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.34540000557899475},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3285999894142151},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3149000108242035},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2939000129699707},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27129998803138733},{"id":"https://openalex.org/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.2669000029563904},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.16438","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16438","pdf_url":"https://arxiv.org/pdf/2608.16438","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.16438","doi":"https://doi.org/10.48550/arxiv.2608.16438","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.16438","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.16438","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16438","pdf_url":"https://arxiv.org/pdf/2608.16438","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G8526296420","display_name":null,"funder_award_id":"2338/23","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203680732.pdf","grobid_xml":"https://content.openalex.org/works/W7203680732.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7167702360","https://openalex.org/W7155765169","https://openalex.org/W6903795504","https://openalex.org/W7164857679","https://openalex.org/W4416050177","https://openalex.org/W4417281706","https://openalex.org/W7214639347","https://openalex.org/W7165658278","https://openalex.org/W7162429359","https://openalex.org/W4404353289"],"abstract_inverted_index":{"In":[0,216],"a":[1,41,107,175,235,239],"world":[2],"where":[3],"valuable":[4,76],"artifacts":[5],"are":[6],"increasingly":[7],"created,":[8],"completed,":[9],"or":[10,47,61,95,207],"processed":[11],"by":[12,90,96,115,126,193,198,200,205,208],"LLMs,":[13],"the":[14,22,31,34,67,80,85,98,118,123,127,141,145,149,172,195,202,219,250,263],"central":[15],"economic":[16],"question":[17],"is":[18,75,227],"not":[19],"only":[20],"what":[21,27],"LLM":[23,53,128],"can":[24],"produce,":[25],"but":[26],"\\emph{value}":[28],"remains":[29],"in":[30,122,156],"inputs":[32],"(i.e.,":[33],"prompts)":[35],"we":[36,65,131],"provide":[37],"to":[38,87,102,112,168,191,218],"it.":[39,104],"Given":[40],"prompt,":[42],"hint,":[43],"critique,":[44],"problem":[45],"statement,":[46],"partial":[48],"solution":[49],"that":[50,70,246,258],"helps":[51],"an":[52,55,73,133,183],"produce":[54],"artifact":[56,82,184],"$z$---a":[57],"proof,":[58],"program,":[59,150],"design,":[60],"scientific":[62],"hypothesis---how":[63],"should":[64],"measure":[66],"value":[68,161,181,241],"of":[69,136,148,180,222,242,259],"input?":[71],"Intuitively,":[72],"input":[74],"when":[77],"it":[78,155,261],"makes":[79,186],"target":[81],"easier":[83],"for":[84,154,182],"model":[86],"generate:":[88],"either":[89],"increasing":[91],"its":[92],"sampling":[93],"probability,":[94],"reducing":[97],"thinking":[99,143],"time":[100],"needed":[101],"find":[103],"We":[105,230],"propose":[106],"computational":[108],"Levin--Kolmogorov":[109,138],"complexity":[110],"approach":[111],"this":[113],"problem,":[114],"appropriately":[116],"replacing":[117],"universal":[119],"Turing":[120],"machine":[121],"classical":[124,220],"definitions":[125],"itself.":[129],"Concretely,":[130],"introduce":[132],"LLM-relative":[134],"notion":[135,221],"\\emph{probabilistic":[137],"complexity}":[139],"$pKt$---treating":[140],"model's":[142],"as":[144,162],"random":[146],"tape":[147],"and":[151,214],"charging":[152],"logarithmically":[153],"Levin's":[157],"manner---and":[158],"define":[159],"prompt":[160,176,240,251],"algorithmic":[163,223],"mutual":[164,224],"information":[165],"with":[166,262],"respect":[167],"$pKt$.":[169],"This":[170],"captures":[171],"intuition":[173],"above:":[174],"having":[177],"$b$":[178],"bits":[179,244],"$z$":[185,187],"$2^b$":[188],"times":[189,257],"``easier":[190],"obtain'',":[192],"multiplying":[194],"success":[196],"probability":[197,213],"$2^b$,":[199,206],"dividing":[201],"required":[203],"computation":[204],"any":[209],"corresponding":[210],"tradeoff":[211],"between":[212],"computation.":[215],"contrast":[217],"information,":[225],"ours":[226],"efficiently":[228],"estimable.":[229],"additionally":[231],"show":[232],"that,":[233],"under":[234],"natural":[236],"reproduction":[237],"experiment,":[238],"\\(b\\)":[243],"means":[245],"reproducing":[247,260],"\\(z\\)":[248],"without":[249],"has":[252],"median":[253],"token":[254],"cost":[255],"\\(2^b\\)":[256],"prompt.":[264]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-19T00:00:00"}
