{"id":"https://openalex.org/W7161268231","doi":"https://doi.org/10.48550/arxiv.2605.15163","title":"Automating Bitvector and Finite Field Equivalence Proofs in Lean","display_name":"Automating Bitvector and Finite Field Equivalence Proofs in Lean","publication_year":2026,"publication_date":"2026-05-14","ids":{"openalex":"https://openalex.org/W7161268231","doi":"https://doi.org/10.48550/arxiv.2605.15163"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.15163","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15163","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":"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.2605.15163","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013549442","display_name":"Elizaveta Pertseva","orcid":"https://orcid.org/0000-0001-9950-672X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pertseva, Elizaveta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084882063","display_name":"Valentin Robert","orcid":"https://orcid.org/0000-0003-2364-1794"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert, Valentin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136199420","display_name":"Clark Barrett","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barrett, Clark","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136247403","display_name":"James Parker","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Parker, James","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":0.6995000243186951,"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":0.6995000243186951,"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/T12122","display_name":"Physical Unclonable Functions (PUFs) and Hardware Security","score":0.16359999775886536,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.03579999879002571,"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/correctness","display_name":"Correctness","score":0.7742000222206116},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6919999718666077},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6305000185966492},{"id":"https://openalex.org/keywords/workflow","display_name":"Workflow","score":0.5537999868392944},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5202000141143799},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4375},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.3905999958515167}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7742000222206116},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6919999718666077},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6305000185966492},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6301000118255615},{"id":"https://openalex.org/C177212765","wikidata":"https://www.wikidata.org/wiki/Q627335","display_name":"Workflow","level":2,"score":0.5537999868392944},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5202000141143799},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4487000107765198},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4375},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3749000132083893},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3695000112056732},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C164155591","wikidata":"https://www.wikidata.org/wiki/Q2067766","display_name":"Satisfiability modulo theories","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.26269999146461487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2565999925136566}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.15163","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15163","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":"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.2605.15163","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15163","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":"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":{"Efforts":[0],"to":[1,78,85],"verify":[2],"Zero-Knowledge":[3],"Proof":[4],"circuit":[5],"encodings":[6],"have":[7],"highlighted":[8],"the":[9,13],"challenge":[10],"of":[11,15,21,45],"proving":[12],"correctness":[14],"quantifier-free":[16],"statements":[17],"that":[18,49,71],"make":[19],"use":[20],"both":[22],"bitvector":[23],"and":[24,55,75],"finite":[25,83],"field":[26],"operations.":[27],"Existing":[28],"verification":[29],"workflows":[30],"are":[31],"either":[32],"manual":[33],"or":[34],"rely":[35],"on":[36,42],"SMT":[37,94],"solvers,":[38,95],"which":[39],"scale":[40],"poorly":[41],"some":[43],"classes":[44],"problems":[46],"for":[47],"reasons":[48],"include":[50],"difficulties":[51],"with":[52,90],"conversion":[53],"operators":[54],"challenges":[56],"reasoning":[57],"about":[58],"inequalities.":[59],"To":[60],"address":[61],"these":[62],"limitations,":[63],"we":[64],"present":[65],"a":[66],"novel":[67],"Lean":[68],"tactic":[69],"BitModEq":[70],"leverages":[72],"range":[73],"lemmas":[74],"case":[76],"analysis":[77],"produce":[79],"verified":[80],"translations":[81],"from":[82],"fields":[84],"bitvectors.":[86],"Our":[87],"approach,":[88],"combined":[89],"bit-blasting,":[91],"outperforms":[92],"state-of-the-art":[93],"solving":[96],"19%":[97],"more":[98],"ZKP":[99],"arithmetization":[100],"benchmarks.":[101]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-16T00:00:00"}
