{"id":"https://openalex.org/W4416626082","doi":"https://doi.org/10.1145/3778245","title":"Towards Deterministic Algorithms for Constant-Depth Factors of Constant-Depth Circuits","display_name":"Towards Deterministic Algorithms for Constant-Depth Factors of Constant-Depth Circuits","publication_year":2025,"publication_date":"2025-11-25","ids":{"openalex":"https://openalex.org/W4416626082","doi":"https://doi.org/10.1145/3778245"},"language":"en","primary_location":{"id":"doi:10.1145/3778245","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3778245","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1145/3778245","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100713973","display_name":"Mrinal Kumar","orcid":"https://orcid.org/0000-0002-6430-0219"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mrinal Kumar","raw_affiliation_strings":["School of Technology and Computer Science, Tata Institute of Fundamental Research","School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0002-6430-0219","affiliations":[{"raw_affiliation_string":"School of Technology and Computer Science, Tata Institute of Fundamental Research","institution_ids":["https://openalex.org/I11947397"]},{"raw_affiliation_string":"School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043140740","display_name":"Varun Ramanathan","orcid":"https://orcid.org/0009-0002-5903-593X"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Varun Ramanathan","raw_affiliation_strings":["School of Technology and Computer Science, Tata Institute of Fundamental Research","School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India"],"raw_orcid":"https://orcid.org/0009-0002-5903-593X","affiliations":[{"raw_affiliation_string":"School of Technology and Computer Science, Tata Institute of Fundamental Research","institution_ids":["https://openalex.org/I11947397"]},{"raw_affiliation_string":"School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070371254","display_name":"Ramprasad Saptharishi","orcid":"https://orcid.org/0000-0002-7485-3220"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ramprasad Saptharishi","raw_affiliation_strings":["School of Technology and Computer Science, Tata Institute of Fundamental Research","School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0002-7485-3220","affiliations":[{"raw_affiliation_string":"School of Technology and Computer Science, Tata Institute of Fundamental Research","institution_ids":["https://openalex.org/I11947397"]},{"raw_affiliation_string":"School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073175433","display_name":"Ben Lee Volk","orcid":"https://orcid.org/0000-0002-7143-7280"},"institutions":[{"id":"https://openalex.org/I2801151526","display_name":"Brandman University","ror":"https://ror.org/013922990","country_code":"US","type":"education","lineage":["https://openalex.org/I2801151526"]},{"id":"https://openalex.org/I4210093787","display_name":"Herzliya Medical Center","ror":"https://ror.org/00m6hsp80","country_code":"IL","type":"healthcare","lineage":["https://openalex.org/I4210093787"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Ben Lee Volk","raw_affiliation_strings":["Reichman University","Reichman University, Herzliya, Israel"],"raw_orcid":"https://orcid.org/0000-0002-7143-7280","affiliations":[{"raw_affiliation_string":"Reichman University","institution_ids":["https://openalex.org/I2801151526"]},{"raw_affiliation_string":"Reichman University, Herzliya, Israel","institution_ids":["https://openalex.org/I4210093787"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32983801,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":"1","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9126999974250793,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9126999974250793,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.021900000050663948,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.011800000444054604,"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/factorization","display_name":"Factorization","score":0.5733000040054321},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5019000172615051},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4846999943256378},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.41780000925064087},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.40709999203681946},{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.3944000005722046},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.3822999894618988},{"id":"https://openalex.org/keywords/combinational-logic","display_name":"Combinational logic","score":0.3239000141620636}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6215999722480774},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5733000040054321},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5626000165939331},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5019000172615051},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.40709999203681946},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.3944000005722046},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.3822999894618988},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36480000615119934},{"id":"https://openalex.org/C81409106","wikidata":"https://www.wikidata.org/wiki/Q76505","display_name":"Combinational logic","level":3,"score":0.3239000141620636},{"id":"https://openalex.org/C187075797","wikidata":"https://www.wikidata.org/wiki/Q173245","display_name":"Sequential logic","level":3,"score":0.32359999418258667},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C108741685","wikidata":"https://www.wikidata.org/wiki/Q392477","display_name":"Factorization of polynomials","level":4,"score":0.30379998683929443},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C190560348","wikidata":"https://www.wikidata.org/wiki/Q3245116","display_name":"Circuit design","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25760000944137573},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C76253118","wikidata":"https://www.wikidata.org/wiki/Q1051983","display_name":"Cyclotomic polynomial","level":3,"score":0.25529998540878296},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3778245","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3778245","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3778245","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3778245","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2000108234","https://openalex.org/W2026036943","https://openalex.org/W2032431003","https://openalex.org/W2054534833","https://openalex.org/W2089272132","https://openalex.org/W2111727595","https://openalex.org/W2141040012","https://openalex.org/W2153445467","https://openalex.org/W2213867208","https://openalex.org/W2293228899","https://openalex.org/W3021415944","https://openalex.org/W3175812362","https://openalex.org/W3207259719","https://openalex.org/W4205630623","https://openalex.org/W4386875904"],"related_works":[],"abstract_inverted_index":{"We":[0],"design":[1],"a":[2,11,17,25,77,81,97,105,112,182],"deterministic":[3],"subexponential":[4],"time":[5],"algorithm":[6,95],"that":[7,38,56,83,125,135,178],"takes":[8],"as":[9,111,196,198],"input":[10,75,194],"multivariate":[12,173],"polynomial":[13,174,195],"f":[14,44,67,103,141],"computed":[15],"by":[16,46],"constant-depth":[18,47,206],"circuit":[19,127,138],"over":[20],"rational":[21],"numbers,":[22],"and":[23,33,104,119,142,161],"outputs":[24],"list":[26,50],"L":[27,51],"of":[28,43,66,93,99,102,117,129,136,140,150,158,172,179,202],"circuits":[29,55],"(of":[30],"unbounded":[31],"depth":[32],"possibly":[34],"with":[35,122,154],"division":[36,78],"gates)":[37],"contains":[39],"all":[40],"irreducible":[41,200],"factors":[42,65],"computable":[45],"circuits.":[48,207],"This":[49,145],"might":[52,148],"also":[53],"include":[54],"are":[57,69],"spurious:":[58],"they":[59],"either":[60],"do":[61],"not":[62,70],"correspond":[63],"to":[64,76,134],"or":[68],"even":[71],"well-defined,":[72],"e.g.,":[73],"the":[74,85,100,115,123,126,130,137,155,190,193,199],"gate":[79],"is":[80,96,132],"sub-circuit":[82],"computes":[84],"identically":[86],"zero":[87],"polynomial.":[88],"The":[89],"key":[90,170],"technical":[91],"ingredient":[92],"our":[94],"notion":[98],"pseudo-resultant":[101,131],"factor":[106,201],"g":[107,118,143],",":[108,121],"which":[109,147],"serves":[110],"proxy":[113],"for":[114,186,189],"resultant":[116],"\\(f/g\\)":[120],"advantage":[124],"complexity":[128,139],"comparable":[133],".":[144],"notion,":[146],"be":[149],"independent":[151],"interest,":[152],"together":[153],"recent":[156],"results":[157],"Limaye,":[159],"Srinivasan,":[160],"Tavenas":[162],"[":[163],"19":[164],"]":[165],"helps":[166],"us":[167],"derandomize":[168],"one":[169],"step":[171],"factorization":[175],"algorithms":[176],"\u2014":[177],"deterministically":[180],"finding":[181],"good":[183],"starting":[184],"point":[185],"Newton":[187],"Iteration":[188],"case":[191],"when":[192],"well":[197],"interest":[203],"have":[204],"small":[205]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-11-25T00:00:00"}
