{"id":"https://openalex.org/W7164042613","doi":"https://doi.org/10.1145/3798129.3800878","title":"Reconstruction of Depth-3 Arithmetic Circuits with Constant Top Fan-In","display_name":"Reconstruction of Depth-3 Arithmetic Circuits with Constant Top Fan-In","publication_year":2026,"publication_date":"2026-06-09","ids":{"openalex":"https://openalex.org/W7164042613","doi":"https://doi.org/10.1145/3798129.3800878"},"language":null,"primary_location":{"id":"doi:10.1145/3798129.3800878","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800878","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3798129.3800878","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020540233","display_name":"Shubhangi Saraf","orcid":"https://orcid.org/0009-0005-0874-2978"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shubhangi Saraf","raw_affiliation_strings":["University of Toronto, Department of Mathematics and Department of Computer Science, Toronto, Canada"],"raw_orcid":"https://orcid.org/0009-0005-0874-2978","affiliations":[{"raw_affiliation_string":"University of Toronto, Department of Mathematics and Department of Computer Science, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001648320","display_name":"Devansh Shringi","orcid":"https://orcid.org/0000-0001-6442-2411"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Devansh Shringi","raw_affiliation_strings":["University of Toronto, Department of Computer Science, Toronto, Canada"],"raw_orcid":"https://orcid.org/0000-0001-6442-2411","affiliations":[{"raw_affiliation_string":"University of Toronto, Department of Computer Science, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075891299","display_name":"Narmada Varadarajan","orcid":"https://orcid.org/0000-0002-1586-3082"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Narmada Varadarajan","raw_affiliation_strings":["University of Toronto, Department of Mathematics, Toronto, Canada"],"raw_orcid":"https://orcid.org/0000-0002-1586-3082","affiliations":[{"raw_affiliation_string":"University of Toronto, Department of Mathematics, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.89972195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1704","last_page":"1715"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.12449999898672104,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.12449999898672104,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.08839999884366989,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.06319999694824219,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5752000212669373},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.4424999952316284},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.30379998683929443},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.28929999470710754},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.27709999680519104}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5952000021934509},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5752000212669373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4893999993801117},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4449000060558319},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.4424999952316284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4058000147342682},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.28929999470710754},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C182775192","wikidata":"https://www.wikidata.org/wiki/Q913725","display_name":"Saturation arithmetic","level":3,"score":0.27140000462532043},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2685999870300293},{"id":"https://openalex.org/C190560348","wikidata":"https://www.wikidata.org/wiki/Q3245116","display_name":"Circuit design","level":2,"score":0.26589998602867126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3798129.3800878","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800878","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3798129.3800878","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800878","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8914706487","display_name":null,"funder_award_id":"RGPIN-2022-04250","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W89122021","https://openalex.org/W1599026900","https://openalex.org/W1838223085","https://openalex.org/W1967348711","https://openalex.org/W1972750117","https://openalex.org/W1974321539","https://openalex.org/W1992781176","https://openalex.org/W2016576580","https://openalex.org/W2019969751","https://openalex.org/W2031554429","https://openalex.org/W2047295759","https://openalex.org/W2050570613","https://openalex.org/W2053997972","https://openalex.org/W2059084795","https://openalex.org/W2060788286","https://openalex.org/W2070279173","https://openalex.org/W2073240615","https://openalex.org/W2080132708","https://openalex.org/W2082387287","https://openalex.org/W2084050956","https://openalex.org/W2087857477","https://openalex.org/W2093103267","https://openalex.org/W2104644213","https://openalex.org/W2128510017","https://openalex.org/W2130196976","https://openalex.org/W2132463883","https://openalex.org/W2142326730","https://openalex.org/W2148132824","https://openalex.org/W2195982063","https://openalex.org/W2904001778","https://openalex.org/W2951498306","https://openalex.org/W2963409396","https://openalex.org/W2963679506","https://openalex.org/W2963854229","https://openalex.org/W2970276273","https://openalex.org/W3021967345","https://openalex.org/W3037624630","https://openalex.org/W3046505869","https://openalex.org/W3140482674","https://openalex.org/W3175812362","https://openalex.org/W3197084549","https://openalex.org/W4233477278","https://openalex.org/W4252861488","https://openalex.org/W4313203173","https://openalex.org/W4399522856","https://openalex.org/W6902806374","https://openalex.org/W6948107546","https://openalex.org/W7109950510","https://openalex.org/W7110000962"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,90],"paper,":[2],"we":[3,36],"give":[4],"the":[5,81,88,92,97,106],"first":[6],"subexponential":[7],"(in":[8],"fact,":[9],"quasi-polynomial":[10],"time)":[11],"reconstruction":[12],"algorithm":[13,63],"for":[14,39],"depth-3":[15],"circuits":[16],"of":[17,56,84],"any":[18,28,40],"constant":[19,41],"top":[20],"fan-in":[21],"(\u03a3\u03a0\u03a3(k)":[22],"circuits)":[23],"over":[24],"\u211d,":[25],"\u2102,":[26,102],"or":[27,101],"large":[29],"characteristic":[30],"finite":[31],"field":[32,98,107],"F.":[33],"More":[34],"explicitly,":[35],"show":[37],"that":[38,64],"k,":[42],"given":[43],"black-box":[44],"access":[45],"to":[46],"an":[47],"n-variate":[48],"polynomial":[49],"f":[50],"computed":[51],"by":[52],"a":[53,61,71],"\u03a3\u03a0\u03a3(k)":[54,73],"circuit":[55,74],"size":[57,78],"s,":[58],"there":[59],"is":[60,91,99,108],"randomized":[62],"runs":[65],"in":[66,87],"time":[67],"quasi-poly(n,s)":[68],"and":[69,103],"outputs":[70],"generalized":[72],"computing":[75],"f.":[76],"The":[77],"s":[79],"includes":[80],"bit":[82,94],"complexity":[83,95],"coefficients":[85],"appearing":[86],"circuit:":[89],"max":[93],"if":[96,105],"\u211d":[100],"log|F|":[104],"finite.":[109]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-06-10T00:00:00"}