{"id":"https://openalex.org/W4417009936","doi":"https://doi.org/10.48550/arxiv.2512.02808","title":"Search versus Decision for $\\mathsf{S}_2^\\mathsf{P}$","display_name":"Search versus Decision for $\\mathsf{S}_2^\\mathsf{P}$","publication_year":2025,"publication_date":"2025-12-02","ids":{"openalex":"https://openalex.org/W4417009936","doi":"https://doi.org/10.48550/arxiv.2512.02808"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2512.02808","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.02808","pdf_url":"https://arxiv.org/pdf/2512.02808","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.02808","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075191567","display_name":"Lance Fortnow","orcid":"https://orcid.org/0000-0002-2020-1358"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fortnow, Lance","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075191567"],"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":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.6739000082015991,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.6739000082015991,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.13030000030994415,"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/T10237","display_name":"Cryptography and Data Security","score":0.02539999969303608,"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/class","display_name":"Class (philosophy)","score":0.6161999702453613},{"id":"https://openalex.org/keywords/decision-problem","display_name":"Decision problem","score":0.5153999924659729},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.47929999232292175},{"id":"https://openalex.org/keywords/search-problem","display_name":"Search problem","score":0.47029998898506165},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4187000095844269},{"id":"https://openalex.org/keywords/decision-theory","display_name":"Decision theory","score":0.38499999046325684},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.376800000667572},{"id":"https://openalex.org/keywords/decision-analysis","display_name":"Decision analysis","score":0.3725999891757965}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6161999702453613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5232999920845032},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.5153999924659729},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.47929999232292175},{"id":"https://openalex.org/C201789804","wikidata":"https://www.wikidata.org/wiki/Q2362762","display_name":"Search problem","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39739999175071716},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.38499999046325684},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.376800000667572},{"id":"https://openalex.org/C186116695","wikidata":"https://www.wikidata.org/wiki/Q5249226","display_name":"Decision analysis","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.3617999851703644},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35440000891685486},{"id":"https://openalex.org/C84839998","wikidata":"https://www.wikidata.org/wiki/Q5249245","display_name":"Decision rule","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C150325174","wikidata":"https://www.wikidata.org/wiki/Q4335500","display_name":"Optimal decision","level":3,"score":0.3361999988555908},{"id":"https://openalex.org/C125583679","wikidata":"https://www.wikidata.org/wiki/Q755673","display_name":"Search algorithm","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C2984634286","wikidata":"https://www.wikidata.org/wiki/Q1331926","display_name":"Decision process","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28119999170303345},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.27799999713897705},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.262800008058548},{"id":"https://openalex.org/C59594135","wikidata":"https://www.wikidata.org/wiki/Q5249242","display_name":"Decision model","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C2986909951","wikidata":"https://www.wikidata.org/wiki/Q330268","display_name":"Decision system","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2512.02808","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.02808","pdf_url":"https://arxiv.org/pdf/2512.02808","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2512.02808","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.02808","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2512.02808","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.02808","pdf_url":"https://arxiv.org/pdf/2512.02808","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"compare":[1],"the":[2,5,11,20,30,37],"complexity":[3,12],"of":[4,39],"search":[6,31,41,57],"and":[7],"decision":[8,21,60],"problems":[9,42],"for":[10,61],"class":[13,38],"S2P.":[14],"While":[15],"Cai":[16],"(2007)":[17],"showed":[18],"that":[19,29],"problem":[22,32],"is":[23,33,67],"contained":[24,68],"in":[25,44,69],"ZPP^NP,":[26],"we":[27],"show":[28],"equivalent":[34],"to":[35,59],"TFNP^NP,":[36],"total":[40],"verifiable":[43],"polynomial":[45],"time":[46],"with":[47],"an":[48],"NP":[49],"oracle.":[50],"This":[51],"highlights":[52],"a":[53],"significant":[54],"contrast:":[55],"if":[56],"reduces":[58],"S2P,":[62],"then":[63],"$\u03a3_2^p":[64],"\\cap":[65],"\u03a0_2^p$":[66],"ZPP^NP.":[70]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-12-04T00:00:00"}