{"id":"https://openalex.org/W4415088200","doi":"https://doi.org/10.48550/arxiv.2509.11349","title":"Efficient Polynomial Identity Testing Over Nonassociative Algebras","display_name":"Efficient Polynomial Identity Testing Over Nonassociative Algebras","publication_year":2025,"publication_date":"2025-09-14","ids":{"openalex":"https://openalex.org/W4415088200","doi":"https://doi.org/10.48550/arxiv.2509.11349"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2509.11349","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.11349","pdf_url":"https://arxiv.org/pdf/2509.11349","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":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/2509.11349","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102818340","display_name":"Partha Mukhopadhyay","orcid":"https://orcid.org/0009-0007-3656-8844"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mukhopadhyay, Partha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019965402","display_name":"C. Ramya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ramya, C","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5119958764","display_name":"Pratik Shastri","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shastri, Pratik","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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.9750999808311462,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9732000231742859,"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/identity","display_name":"Identity (music)","score":0.6229000091552734},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6060000061988831},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5550000071525574},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5335000157356262},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5109000205993652},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45080000162124634}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8030999898910522},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.6229000091552734},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6060000061988831},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5550000071525574},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5335000157356262},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5109000205993652},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4828999936580658},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35339999198913574},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C52153879","wikidata":"https://www.wikidata.org/wiki/Q930499","display_name":"Symmetric polynomial","level":4,"score":0.2881999909877777},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.28299999237060547},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2606000006198883}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2509.11349","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.11349","pdf_url":"https://arxiv.org/pdf/2509.11349","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2509.11349","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.11349","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":"pmh:oai:arXiv.org:2509.11349","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.11349","pdf_url":"https://arxiv.org/pdf/2509.11349","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":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":[0,64],"design":[1],"the":[2,10,18,30,53,61,83,114,133,143,150,171,179],"first":[3,84],"efficient":[4],"polynomial":[5,12,90],"identity":[6,54,122,175],"testing":[7,55,123],"algorithms":[8,102],"over":[9,36,88,109],"nonassociative":[11,66,89,104,126,161],"algebra.":[13],"In":[14,149],"particular,":[15],"multiplication":[16],"among":[17],"formal":[19],"variables":[20],"is":[21,25],"commutative":[22,69],"but":[23],"it":[24],"not":[26],"associative.":[27],"This":[28],"complements":[29],"strong":[31],"lower":[32],"bound":[33],"results":[34,59],"obtained":[35],"this":[37],"algebra":[38],"by":[39,129,164],"Hrube\u0161,":[40],"Yehudayoff,":[41],"and":[42,45,49,70],"Wigderson":[43],"(2010)":[44],"Fijalkow,":[46],"Lagarde,":[47],"Ohlmann,":[48],"Serre":[50],"(2021)":[51],"from":[52],"perspective.":[56],"Our":[57],"main":[58],"are":[60],"following:":[62],"(1)":[63],"construct":[65,154],"algebras":[67],"(both":[68],"noncommutative)":[71],"which":[72,106],"have":[73],"no":[74],"low":[75],"degree":[76],"identities.":[77],"As":[78,92],"a":[79,93,119,155],"result,":[80],"we":[81,96,117,153],"obtain":[82,97],"Amitsur-Levitzki":[85],"type":[86],"theorems":[87],"algebras.":[91,111],"direct":[94],"consequence,":[95],"randomized":[98,180],"polynomial-time":[99,121],"black-box":[100,151,172],"PIT":[101],"for":[103,125,160],"polynomials":[105,127,162],"allow":[107],"evaluation":[108],"such":[110,137],"(2)":[112],"On":[113],"derandomization":[115],"side,":[116],"give":[118],"deterministic":[120],"algorithm":[124,139],"given":[128],"arithmetic":[130,165],"circuits":[131,166],"in":[132,178],"white-box":[134],"setting.":[135],"Previously,":[136],"an":[138],"was":[140,182],"known":[141],"with":[142],"additional":[144],"restriction":[145],"of":[146,158,167,174],"noncommutativity.":[147],"(3)":[148],"setting,":[152,181],"hitting":[156],"set":[157],"quasipolynomial-size":[159],"computed":[163],"small":[168],"depth.":[169],"Understanding":[170],"complexity":[173],"testing,":[176],"even":[177],"open":[183],"prior":[184],"to":[185],"our":[186],"work.":[187]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-12T00:00:00"}
