{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:27:15Z","timestamp":1774625235644,"version":"3.50.1"},"reference-count":13,"publisher":"Elsevier BV","issue":"6","license":[{"start":{"date-parts":[[1997,9,1]],"date-time":"1997-09-01T00:00:00Z","timestamp":873072000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information Processing Letters"],"published-print":{"date-parts":[[1997,9]]},"DOI":"10.1016\/s0020-0190(97)00141-5","type":"journal-article","created":{"date-parts":[[2003,4,23]],"date-time":"2003-04-23T20:36:00Z","timestamp":1051130160000},"page":"287-293","source":"Crossref","is-referenced-by-count":15,"title":["On the power of a threshold gate at the top"],"prefix":"10.1016","volume":"63","author":[{"given":"Mikael","family":"Goldmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/S0020-0190(97)00141-5_BIB1","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1137\/0403015","article-title":"Harmonic analysis of polynomial threshold functions","volume":"3","author":"Bruck","year":"1990","journal-title":"SIAM J. Discrete Math."},{"key":"10.1016\/S0020-0190(97)00141-5_BIB2","series-title":"Real Analysis and Probability","author":"Dudley","year":"1989"},{"key":"10.1016\/S0020-0190(97)00141-5_BIB3","series-title":"Workshop on Computational Learning Theory","first-page":"202","article-title":"Boosting a weak learning algorithm by majority","author":"Freund","year":"1990"},{"key":"10.1016\/S0020-0190(97)00141-5_BIB4","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/BF01200426","article-title":"Majority gates vs. general weighted threshold gates","volume":"2","author":"Goldmann","year":"1992","journal-title":"Comput. Complexity"},{"key":"10.1016\/S0020-0190(97)00141-5_BIB5","series-title":"Proc. 5th Ann. Structure in Complexity Theory Conf.","first-page":"295","article-title":"An oracle separating \u2295P from PPPH","author":"Green","year":"1990"},{"key":"10.1016\/S0020-0190(97)00141-5_BIB6","series-title":"Proc. 28th IEEE Symp. on Foundations of Computer Science","first-page":"99","article-title":"Threshold circuits of bounded depth","author":"Hajnal","year":"1987"},{"key":"10.1016\/S0020-0190(97)00141-5_BIB7","series-title":"Computational Limitations of Small-Depth Circuits","author":"H\u00e5stad","year":"1986"},{"issue":"2","key":"10.1016\/S0020-0190(97)00141-5_BIB8","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF01272517","article-title":"On the power of small-depth threshold circuits","volume":"1","author":"H\u00e5stad","year":"1991","journal-title":"Comput. Complexity"},{"key":"10.1016\/S0020-0190(97)00141-5_BIB9","unstructured":"M. Krause, Private communication, 1993."},{"key":"10.1016\/S0020-0190(97)00141-5_BIB10","series-title":"Proc. 26th ACM Symp. on Theory of Computing","first-page":"48","article-title":"On the computational power of threshold circuits with MOD-gates","author":"Krause","year":"1994"},{"key":"10.1016\/S0020-0190(97)00141-5_BIB11","series-title":"Proc. 32th IEEE Symp. on Foundations of Computer Science","first-page":"777","article-title":"Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fan-in","author":"Krause","year":"1991"},{"issue":"6","key":"10.1016\/S0020-0190(97)00141-5_BIB12","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0020-0190(93)90041-7","article-title":"n\u03a9(log n) lower bounds on the size of depth 3 threshold circuits with AND gates at the bottom","volume":"45","author":"Razborov","year":"1993","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/S0020-0190(97)00141-5_BIB13","doi-asserted-by":"crossref","unstructured":"K.Y. Siu and V. Roychowdhury, On optimal depth threshold circuits for multiplication and related problems, SIAM J. Discrete Math., to appear.","DOI":"10.1137\/S0895480192228619"}],"container-title":["Information Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0020019097001415?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0020019097001415?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T16:54:21Z","timestamp":1556643261000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0020019097001415"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,9]]},"references-count":13,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1997,9]]}},"alternative-id":["S0020019097001415"],"URL":"https:\/\/doi.org\/10.1016\/s0020-0190(97)00141-5","relation":{},"ISSN":["0020-0190"],"issn-type":[{"value":"0020-0190","type":"print"}],"subject":[],"published":{"date-parts":[[1997,9]]}}}