Approaching the Chasm at Depth Four
Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp (ω(√ n log n )) lower bound for depth four homogeneous circuits computing the permanent with bottom layer of × gates having fanin bounded by √n translates to a superpolynomial lower bound for general arithmet...
Saved in:
| Published in | Journal of the ACM Vol. 61; no. 6; pp. 1 - 16 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Association for Computing Machinery
01.11.2014
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0004-5411 1557-735X |
| DOI | 10.1145/2629541 |
Cover
| Abstract | Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp (ω(√ n log n )) lower bound for depth four homogeneous circuits computing the permanent with bottom layer of × gates having fanin bounded by √n translates to a superpolynomial lower bound for general arithmetic circuits computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via such homogeneous depth four circuits with bounded bottom fanin.
We show here that any homogeneous depth four arithmetic circuit with bottom fanin bounded by √n computing the permanent (or the determinant) must be of size exp,(Ω(√ n )). |
|---|---|
| AbstractList | Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp ( omega ([radic]n log n)) lower bound for depth four homogeneous circuits computing the permanent with bottom layer of gates having fanin bounded by [radic]n translates to a superpolynomial lower bound for general arithmetic circuits computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via such homogeneous depth four circuits with bounded bottom fanin. We show here that any homogeneous depth four arithmetic circuit with bottom fanin bounded by [radic]n computing the permanent (or the determinant) must be of size exp,( Omega ([radic]n)). Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp (ω(√ n log n )) lower bound for depth four homogeneous circuits computing the permanent with bottom layer of × gates having fanin bounded by √n translates to a superpolynomial lower bound for general arithmetic circuits computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via such homogeneous depth four circuits with bounded bottom fanin. We show here that any homogeneous depth four arithmetic circuit with bottom fanin bounded by √n computing the permanent (or the determinant) must be of size exp,(Ω(√ n )). Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp (...(...n log n)) lower bound for depth four homogeneous circuits computing the permanent with bottom layer of x gates having fanin bounded by ...n translates to a superpolynomial lower bound for general arithmetic circuits computing the permanent. Motivated by this, this paper examines the complexity of computing the permanent and determinant via such homogeneous depth four circuits with bounded bottom fanin. It shows here that any homogeneous depth four arithmetic circuit with bottom fanin bounded by vn computing the permanent (or the determinant) must be of size exp,(...(...n)). (ProQuest: ... denotes formulae/symbols omitted.) |
| Author | Gupta, Ankit Saptharishi, Ramprasad Kamath, Pritish Kayal, Neeraj |
| Author_xml | – sequence: 1 givenname: Ankit surname: Gupta fullname: Gupta, Ankit organization: Microsoft Research, India – sequence: 2 givenname: Pritish surname: Kamath fullname: Kamath, Pritish organization: Microsoft Research, India – sequence: 3 givenname: Neeraj surname: Kayal fullname: Kayal, Neeraj organization: Microsoft Research, India – sequence: 4 givenname: Ramprasad surname: Saptharishi fullname: Saptharishi, Ramprasad organization: Chennai Mathematical Institute, Cambridge, MA |
| BookMark | eNpl0E1LAzEQBuAgFWyr-BcWetDLar4mH8dSWxUKXhS8hTRN3S3b3TXJHvz3RtpTPQ0zPAwv7wSN2q71CN0S_EAIh0cqqAZOLtCYAMhSMvgcoTHGmJf5TK7QJMZ9XjHFcoxm874PnXVV3X4VqfLForLxUNhUPPk-VcWqG8I1utzZJvqb05yij9XyffFSrt-eXxfzdemoEqlUUlHKt3xjnWdaaCodpxvthQbYOBBScM41IwoIUyC2fCeEsNKC09oxydkU3R__5kTfg4_JHOrofNPY1ndDNERhRShwhTOdndF9DtrmdIYIppTGlEFW5VG50MUY_M64OtlUd20Ktm4MweavMnOqLPu7M9-H-mDDzz_5C_eMZ1U |
| CODEN | JACOAH |
| CitedBy_id | crossref_primary_10_1007_s00037_018_0171_9 crossref_primary_10_1007_s00493_019_4009_0 crossref_primary_10_1145_3313232 crossref_primary_10_1007_s00037_021_00214_1 crossref_primary_10_1145_3611094 crossref_primary_10_1145_3544979_3544989 crossref_primary_10_1007_s00037_019_00189_0 crossref_primary_10_1145_3460952 crossref_primary_10_1137_140999220 crossref_primary_10_1137_18M1173319 crossref_primary_10_1145_3170709 crossref_primary_10_1137_140957123 crossref_primary_10_1145_2852040_2852051 crossref_primary_10_1145_3065470 crossref_primary_10_1145_3689957 |
| Cites_doi | 10.1007/PL00001609 10.1145/2591796.2591824 10.1109/CCC.2013.10 10.1145/276698.276872 10.1007/s002009900021 10.1016/0021-8693(86)90134-1 10.1016/j.tcs.2012.03.041 10.1007/978-3-642-40313-2_71 10.1145/800135.804419 10.1145/1502793.1502797 10.1007/BF01294256 10.1080/00927879008824043 10.1109/FOCS.2008.32 10.1007/BF02571229 10.1145/2213977.2214036 10.1145/2591796.2591847 10.1080/00029890.2000.12005235 10.1109/CCC.2008.8 |
| ContentType | Journal Article |
| Copyright | Copyright Association for Computing Machinery Nov 2014 |
| Copyright_xml | – notice: Copyright Association for Computing Machinery Nov 2014 |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1145/2629541 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts CrossRef Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1557-735X |
| EndPage | 16 |
| ExternalDocumentID | 3533512241 10_1145_2629541 |
| Genre | Feature |
| GroupedDBID | --Z -DZ -~X .DC 29L 3R3 4.4 5GY 5VS 85S 8US 8VB AAHTB AAIKC AAKMM AALFJ AAMNW AAYFX AAYXX ABCQX ABFSI ABPEJ ABPPZ ACGOD ACM ACNCT ADBCU ADL ADMLS AEBYY AEFXT AEGXH AEJOY AEMOZ AENEX AENSD AFWIH AFWXC AGHSJ AHQJS AIKLT AKRVB AKVCP ALMA_UNASSIGNED_HOLDINGS AMVHM ASPBG AVWKF BDXCO CCLIF CITATION CS3 D0L DU5 EBS EJD FEDTE GUFHI HGAVV H~9 IAO ICD IEA IOF K1G L7B LHSKQ P1C PQQKQ QWB RNS TAE TH9 TN5 UKR UPT WH7 XSW YQT ZCA ZL0 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c286t-878224d4bace396927c42b9e6955bc56764449318513856d4f666a7a5c99c3743 |
| ISSN | 0004-5411 |
| IngestDate | Fri Jul 11 16:47:55 EDT 2025 Mon Jun 30 05:39:32 EDT 2025 Tue Aug 05 12:04:00 EDT 2025 Thu Apr 24 23:10:23 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c286t-878224d4bace396927c42b9e6955bc56764449318513856d4f666a7a5c99c3743 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| PQID | 1638890235 |
| PQPubID | 47580 |
| PageCount | 16 |
| ParticipantIDs | proquest_miscellaneous_1808125480 proquest_journals_1638890235 crossref_citationtrail_10_1145_2629541 crossref_primary_10_1145_2629541 |
| PublicationCentury | 2000 |
| PublicationDate | 2014-11-01 |
| PublicationDateYYYYMMDD | 2014-11-01 |
| PublicationDate_xml | – month: 11 year: 2014 text: 2014-11-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Journal of the ACM |
| PublicationYear | 2014 |
| Publisher | Association for Computing Machinery |
| Publisher_xml | – name: Association for Computing Machinery |
| References | e_1_2_1_7_1 e_1_2_1_8_1 e_1_2_1_20_1 e_1_2_1_5_1 e_1_2_1_6_1 e_1_2_1_3_1 e_1_2_1_4_1 e_1_2_1_13_1 e_1_2_1_1_1 e_1_2_1_10_1 e_1_2_1_21_1 e_1_2_1_2_1 e_1_2_1_11_1 e_1_2_1_16_1 e_1_2_1_17_1 e_1_2_1_14_1 e_1_2_1_15_1 Kumar Mrinal (e_1_2_1_12_1) 2013; 20 e_1_2_1_9_1 e_1_2_1_18_1 e_1_2_1_19_1 |
| References_xml | – ident: e_1_2_1_18_1 doi: 10.1007/PL00001609 – ident: e_1_2_1_4_1 doi: 10.1145/2591796.2591824 – ident: e_1_2_1_7_1 doi: 10.1109/CCC.2013.10 – ident: e_1_2_1_5_1 doi: 10.1145/276698.276872 – ident: e_1_2_1_6_1 doi: 10.1007/s002009900021 – ident: e_1_2_1_13_1 doi: 10.1016/0021-8693(86)90134-1 – ident: e_1_2_1_3_1 – ident: e_1_2_1_11_1 doi: 10.1016/j.tcs.2012.03.041 – ident: e_1_2_1_20_1 doi: 10.1007/978-3-642-40313-2_71 – ident: e_1_2_1_21_1 doi: 10.1145/800135.804419 – ident: e_1_2_1_15_1 doi: 10.1145/1502793.1502797 – volume: 20 start-page: 68 year: 2013 ident: e_1_2_1_12_1 article-title: Lower bounds for depth 4 homogenous circuits with bounded top fanin publication-title: Electronic Colloquium on Computational Complexity (ECCC) – ident: e_1_2_1_14_1 doi: 10.1007/BF01294256 – ident: e_1_2_1_2_1 doi: 10.1080/00927879008824043 – ident: e_1_2_1_1_1 doi: 10.1109/FOCS.2008.32 – ident: e_1_2_1_19_1 doi: 10.1007/BF02571229 – ident: e_1_2_1_8_1 doi: 10.1145/2213977.2214036 – ident: e_1_2_1_9_1 – ident: e_1_2_1_10_1 doi: 10.1145/2591796.2591847 – ident: e_1_2_1_17_1 doi: 10.1080/00029890.2000.12005235 – ident: e_1_2_1_16_1 doi: 10.1109/CCC.2008.8 |
| SSID | ssj0000207 |
| Score | 2.361078 |
| Snippet | Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp (ω(√ n log n )) lower bound for depth four homogeneous circuits... Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp (...(...n log n)) lower bound for depth four homogeneous circuits... Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp ( omega ([radic]n log n)) lower bound for depth four homogeneous... |
| SourceID | proquest crossref |
| SourceType | Aggregation Database Enrichment Source Index Database |
| StartPage | 1 |
| SubjectTerms | Arithmetic Circuits Complexity Complexity theory Computation Computer science Determinants Gates (circuits) Lower bounds Mathematical analysis Polynomials Studies |
| Title | Approaching the Chasm at Depth Four |
| URI | https://www.proquest.com/docview/1638890235 https://www.proquest.com/docview/1808125480 |
| Volume | 61 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwELaW9sKF0gJi24KMQFxQQHH8iE9otRRVlHKAVtpbZDuuCm3T1TZ7aH89M7HzaAtq4RJFsR0r-ZJvxo9vhpA3aVlaVUqTQKlMgCV1ovPMJnmW2_IIxiCm0XHvf5O7h_zLTMxGo4-DXUvL2r53V3_UlfwPqnANcEWV7D8g290ULsA54AtHQBiO98J4EgOCt5Kn6bHBlBc1sMi8PsaUSYu_OJ-NoGTaR8dfzoMXOalOfnYbYfYMuLNh2iWEPuoLLk3YSu39wvzqZmkM9IpJDZtEwe--m7P5wlyYcjizkPIosRuyJU8Ej2ToI0EKlahMzIYMKtPBlzKkw3RgV4Ok8jZjcwxuwSSuN6a9UWoX4m_Yqm4HYdBTiyI2fEBWmVK4Tr86-bT_9UdvjFlQzLePEnTT2PRDbHrdIblujxsn4-AxeRQBopMA9ToZ-WqDrLWZN2gk4ifk9QB5CljSBnlqatogTxH5p-Tw887BdDeJ6S4Sx3JZg13CHb0lt8b5TEvNlOPMai-1ENYJqcB15RrV7mmWC1nyIxh6GmWE09pl4Ak-IyvVeeWfE8qAVuEvU9Dec8ksnileptJpGB-qfEzets9cuBgLHlOSnBY33uuY0K7iPIQ_uV1lu31pRfw3Lgr08nEFOxNj8qorBubC5ShT-fMl1MGkLwzjDW7e3csWedh_ottkpV4s_QtwB2v7MkL-G4a-WXo |
| linkProvider | EBSCOhost |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Approaching+the+Chasm+at+Depth+Four&rft.jtitle=Journal+of+the+ACM&rft.au=Gupta%2C+Ankit&rft.au=Kamath%2C+Pritish&rft.au=Kayal%2C+Neeraj&rft.au=Saptharishi%2C+Ramprasad&rft.date=2014-11-01&rft.issn=0004-5411&rft.eissn=1557-735X&rft.volume=61&rft.issue=6&rft.spage=1&rft.epage=16&rft_id=info:doi/10.1145%2F2629541&rft.externalDBID=n%2Fa&rft.externalDocID=10_1145_2629541 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0004-5411&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0004-5411&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0004-5411&client=summon |