{"id":"https://openalex.org/W7216548465","doi":"https://doi.org/10.48550/arxiv.2610.01527","title":"Exact Distinguishability in Non-Markovian Decision Processes","display_name":"Exact Distinguishability in Non-Markovian Decision Processes","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216548465","doi":"https://doi.org/10.48550/arxiv.2610.01527"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.01527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01527","pdf_url":"https://arxiv.org/pdf/2610.01527","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.01527","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143504689","display_name":"Kabir Murjani","orcid":"https://orcid.org/0009-0006-3932-5971","observed_orcids":["https://orcid.org/0009-0006-3932-5971"]},"institutions":[{"id":"https://openalex.org/I165831266","display_name":"Nirma University","ror":"https://ror.org/05qkq7x38","country_code":"IN","type":"education","lineage":["https://openalex.org/I165831266"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Murjani, Kabir","raw_affiliation_strings":["Nirma University Ahmedabad , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nirma University Ahmedabad , India","institution_ids":["https://openalex.org/I165831266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5154810555","display_name":"Nisarg Patel","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165831266","display_name":"Nirma University","ror":"https://ror.org/05qkq7x38","country_code":"IN","type":"education","lineage":["https://openalex.org/I165831266"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Patel, Nisarg","raw_affiliation_strings":["Mountain View , CA","Nirma University Ahmedabad , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mountain View , CA","institution_ids":[]},{"raw_affiliation_string":"Nirma University Ahmedabad , India","institution_ids":["https://openalex.org/I165831266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165831266"],"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.7689999938011169,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.7689999938011169,"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/T10142","display_name":"Formal Methods in Verification","score":0.11599999666213989,"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/T11567","display_name":"semigroups and automata theory","score":0.019500000402331352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/non-markovian-environments","display_name":"non-Markovian environments","score":0.8709999918937683},{"id":"https://openalex.org/keywords/distinguishability","display_name":"distinguishability","score":0.6290000081062317},{"id":"https://openalex.org/keywords/observational-equivalence","display_name":"observational equivalence","score":0.6039999723434448},{"id":"https://openalex.org/keywords/posterior-odds","display_name":"posterior odds","score":0.800000011920929},{"id":"https://openalex.org/keywords/behavior-policy","display_name":"behavioral public policy","score":0.7139999866485596},{"id":"https://openalex.org/keywords/finite-state-machines","display_name":"finite automata","score":0.7580000162124634},{"id":"https://openalex.org/keywords/formal-verification","display_name":"formal verification","score":0.6069999933242798},{"id":"https://openalex.org/keywords/lean-4","display_name":"Lean 4","score":0.9419999718666077}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6492000222206116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5318999886512756},{"id":"https://openalex.org/C143095724","wikidata":"https://www.wikidata.org/wiki/Q515895","display_name":"Odds","level":3,"score":0.5174999833106995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4438000023365021},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4153999984264374},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31869998574256897},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31049999594688416},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28630000352859497},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2508000135421753},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.01527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01527","pdf_url":"https://arxiv.org/pdf/2610.01527","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.2610.01527","doi":"https://doi.org/10.48550/arxiv.2610.01527","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.01527","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:2610.01527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01527","pdf_url":"https://arxiv.org/pdf/2610.01527","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/W7216548465.pdf","grobid_xml":"https://content.openalex.org/works/W7216548465.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2966174181","https://openalex.org/W4393090921","https://openalex.org/W4403160410","https://openalex.org/W4387171273","https://openalex.org/W3009415314","https://openalex.org/W2945880240","https://openalex.org/W7010297083","https://openalex.org/W4393146689","https://openalex.org/W7006705873","https://openalex.org/W4225358738"],"abstract_inverted_index":{"Non-Markovian":[0],"environments":[1],"are":[2],"often":[3],"modeled":[4],"as":[5],"Regular":[6],"Decision":[7],"Processes":[8],"(RDPs),":[9],"where":[10],"dynamics":[11],"depend":[12],"on":[13,27,31,137],"the":[14,32,43,51,73,83,92,124,127,145],"interaction":[15],"history":[16],"through":[17],"a":[18,28,61],"finite":[19],"automaton.":[20,129],"Existing":[21],"offline":[22],"guarantees":[23],"for":[24],"RDPs":[25],"rely":[26],"distinguishability":[29,131],"assumption":[30,44,132],"behaviour":[33,63],"policy":[34,64,93],"but":[35],"provide":[36],"no":[37],"means":[38],"of":[39,126,133,139],"verifying":[40],"it.":[41],"When":[42],"is":[45],"violated,":[46],"distinct":[47],"models":[48],"may":[49],"explain":[50],"data":[52,58],"equally":[53],"well.":[54],"We":[55,70,106],"study":[56],"when":[57,91],"collected":[59],"under":[60],"fixed":[62],"can":[65],"distinguish":[66],"two":[67],"candidate":[68],"RDPs.":[69],"prove":[71],"that":[72,117],"posterior":[74],"odds":[75,85],"between":[76],"observationally":[77],"equivalent":[78],"candidates":[79],"remain":[80],"equal":[81],"to":[82],"prior":[84,134],"at":[86],"every":[87,95],"sample":[88],"size,":[89],"even":[90],"visits":[94],"automaton":[96],"state,":[97],"and":[98,112,144],"verify":[99],"both":[100],"results":[101],"formally":[102],"in":[103,120,123,152],"Lean":[104],"4.":[105],"then":[107],"characterize":[108],"this":[109],"equivalence":[110],"exactly":[111],"derive":[113],"PEC,":[114],"an":[115],"algorithm":[116],"decides":[118],"it":[119,151],"time":[121],"linear":[122],"size":[125],"product":[128],"The":[130],"work":[135],"fails":[136],"three":[138],"our":[140],"four":[141],"test":[142],"environments,":[143],"experiment":[146],"identified":[147],"by":[148],"PEC":[149],"restores":[150],"each":[153],"case.":[154]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-03T00:00:00"}