{"id":"https://openalex.org/W7213407443","doi":"https://doi.org/10.48550/arxiv.2609.16173","title":"Exact Complexity of the Satisfiability Problem for Strategy Logic","display_name":"Exact Complexity of the Satisfiability Problem for Strategy Logic","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213407443","doi":"https://doi.org/10.48550/arxiv.2609.16173"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16173","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16173","pdf_url":"https://arxiv.org/pdf/2609.16173","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":null,"license_id":null,"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/2609.16173","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017810424","display_name":"Tikhon Pshenitsyn","orcid":"https://orcid.org/0000-0003-4779-3143","observed_orcids":["https://orcid.org/0000-0003-4779-3143"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pshenitsyn, Tikhon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5017810424"],"corresponding_institution_ids":[],"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.54830002784729,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.54830002784729,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.17720000445842743,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.09920000284910202,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/strategy-logic","display_name":"strategy logic","score":0.972000002861023},{"id":"https://openalex.org/keywords/satisfiability","display_name":"satisfiability","score":0.9589999914169312},{"id":"https://openalex.org/keywords/computational-complexity","display_name":"computational complexity","score":0.7760000228881836},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"second-order arithmetic","score":0.9049999713897705},{"id":"https://openalex.org/keywords/omega-rule","display_name":"omega-rule","score":0.8100000023841858},{"id":"https://openalex.org/keywords/modal-logic","display_name":"modal logic","score":0.4269999861717224}],"concepts":[{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6721000075340271},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.6359999775886536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5787000060081482},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.43650001287460327},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3926999866962433},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3871000111103058},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38040000200271606},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3763999938964844},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.3508000075817108},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.3336000144481659},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.26339998841285706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16173","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16173","pdf_url":"https://arxiv.org/pdf/2609.16173","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.16173","doi":"https://doi.org/10.48550/arxiv.2609.16173","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16173","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:2609.16173","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16173","pdf_url":"https://arxiv.org/pdf/2609.16173","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213407443.pdf","grobid_xml":"https://content.openalex.org/works/W7213407443.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2559113132","https://openalex.org/W2903954122","https://openalex.org/W1500966831","https://openalex.org/W97887531","https://openalex.org/W4386143373","https://openalex.org/W7095817191","https://openalex.org/W2166338730","https://openalex.org/W7101001458","https://openalex.org/W4237879150","https://openalex.org/W2898465663"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,32],"satisfiability":[4],"problem":[5],"for":[6,31],"Strategy":[7,37,40],"Logic":[8,41],"introduced":[9],"by":[10],"Mogavero,":[11],"Murano,":[12],"and":[13],"Vardi":[14],"is":[15,29,42],"$\u03a0^1_\\infty$-complete,":[16],"and,":[17],"more":[18],"strongly,":[19],"computably":[20],"isomorphic":[21],"to":[22],"true":[23],"second-order":[24],"arithmetic.":[25],"The":[26],"lower":[27],"bound":[28],"established":[30],"next-time":[33],"Boolean-goal":[34],"fragment":[35],"of":[36],"Logic.":[38],"Consequently,":[39],"not":[43],"recursively":[44],"axiomatizable,":[45],"even":[46],"with":[47],"effectively":[48],"defined":[49],"$\u03c9$-rules.":[50]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-17T00:00:00"}