{"id":"https://openalex.org/W7129771796","doi":"https://doi.org/10.48550/arxiv.2602.14573","title":"Polar: An Algebraic Analyzer for (Probabilistic) Loops","display_name":"Polar: An Algebraic Analyzer for (Probabilistic) Loops","publication_year":2026,"publication_date":"2026-02-16","ids":{"openalex":"https://openalex.org/W7129771796","doi":"https://doi.org/10.48550/arxiv.2602.14573"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.14573","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14573","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.14573","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061232407","display_name":"Marcel Moosbrugger","orcid":"https://orcid.org/0000-0002-2006-3741"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Moosbrugger, Marcel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092031110","display_name":"Julian M\u00fcllner","orcid":"https://orcid.org/0009-0006-2909-2297"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M\u00fcllner, Julian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126258882","display_name":"Ezio Bartocci","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bartocci, Ezio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Kov\u00e1cs, Laura","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kov\u00e1cs, Laura","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":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.5425000190734863,"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/T10142","display_name":"Formal Methods in Verification","score":0.5425000190734863,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.0892999991774559,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.08309999853372574,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.6610999703407288},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6506999731063843},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.6159999966621399},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6093999743461609},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.5238999724388123},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5145999789237976},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.41440001130104065},{"id":"https://openalex.org/keywords/polar-coordinate-system","display_name":"Polar coordinate system","score":0.40369999408721924}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6610999703407288},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6506999731063843},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.6159999966621399},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6093999743461609},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5309000015258789},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.5238999724388123},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5145999789237976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4823000133037567},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.41440001130104065},{"id":"https://openalex.org/C40069579","wikidata":"https://www.wikidata.org/wiki/Q62494","display_name":"Polar coordinate system","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38760000467300415},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.352400004863739},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3174000084400177},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29339998960494995},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.27250000834465027},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.14573","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14573","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.14573","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14573","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"the":[2,8,31,89,96,133],"Polar":[3,22,66,87,105,137],"framework":[4],"for":[5,132],"fully":[6],"automating":[7],"analysis":[9,82],"of":[10,42,48,53,92,118,126,135,147,149],"classical":[11],"and":[12,57,75,109],"probabilistic":[13,69],"loops":[14,70],"using":[15],"algebraic":[16,26],"reasoning.":[17],"The":[18],"central":[19],"theme":[20],"in":[21,122],"comes":[23],"with":[24,61],"handling":[25],"recurrences":[27,49,93],"that":[28],"precisely":[29],"capture":[30],"loop":[32,59,81],"semantics.":[33],"To":[34,128],"this":[35],"end,":[36],"our":[37],"work":[38],"implements":[39],"a":[40],"variety":[41],"techniques":[43,143],"to":[44,63,94,101,144],"compute":[45,95,145],"exact":[46],"closed-forms":[47,91],"over":[50],"higher-order":[51],"moments":[52,146],"variables,":[54],"infer":[55,102],"invariants,":[56],"derive":[58],"sensitivities":[60],"respect":[62],"unknown":[64],"parameters.":[65],"can":[67],"analyze":[68],"containing":[71],"if-statements,":[72],"polynomial":[73,98],"arithmetic,":[74],"common":[76],"probability":[77],"distributions.":[78],"By":[79],"translating":[80],"into":[83],"linear":[84],"recurrence":[85],"solving,":[86],"uses":[88],"derived":[90],"strongest":[97],"invariant":[99],"or":[100],"parameter":[103],"sensitivity.":[104],"is":[106],"both":[107],"sound":[108,142],"complete":[110],"within":[111],"well-defined":[112],"programming":[113],"model":[114],"restrictions.":[115],"Lifting":[116],"any":[117],"these":[119],"restrictions":[120],"results":[121],"significant":[123],"hardness":[124],"limits":[125],"computation.":[127],"overcome":[129],"computational":[130],"burdens":[131],"sake":[134],"efficiency,":[136],"also":[138],"provides":[139],"incomplete":[140],"but":[141],"combinations":[148],"variables.":[150]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-02-18T00:00:00"}
