{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:38:18Z","timestamp":1787337498692,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>\n                    We prove that a monotone circuit of size n\n                    <jats:sup>d<\/jats:sup>\n                    recognizing connectivity must have depth $\\Omega((\\log n)^2\/\\log d)$. For formulas this implies depth $\\Omega((\\log n)^2\/\\log\\log n)$. For polynomial-size circuits the bound becomes $\\Omega((\\log n)^2)$ which is optimal up to a constant.\n                  <\/jats:p>","DOI":"10.1137\/s0097539795285631","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1283-1294","source":"Crossref","is-referenced-by-count":5,"title":["Monotone Circuits for Connectivity Have Depth (log n)\n                    <sup>2-o(1)<\/sup>"],"prefix":"10.1137","volume":"27","author":[{"given":"Mikael","family":"Goldmann","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johan","family":"H\u00e5stad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579196"},{"key":"R2","first-page":"1033","volume":"282","author":"Andreev A.","year":"1985","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/1948.001.0001"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0403021"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01137685"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01137685"},{"key":"R6","first-page":"798","volume":"281","author":"Razborov A.","year":"1985","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"R7","first-page":"0","volume":"37","author":"Razborov A.","year":"1985","journal-title":"Mat. Zametki"},{"key":"R8","unstructured":"R. Smolensky,\n                      Algebraic methods in the theory of lower bounds for boolean circuit complexity\n                      , in 19, New York, 1987, pp. 77\u201382."},{"key":"R9","unstructured":"Avi Wigderson, The complexity of graph connectivity, Lecture Notes in Comput. Sci., Vol. 629, Springer, Berlin, 1992, 112\u201313294j:05130"},{"key":"R10","unstructured":"Andrew Yao, A lower bound for the monotone depth of connectivity, IEEE Comput. Soc. Press, Los Alamitos, CA, 1994, 302\u20133081489244"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539795285631","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:14:09Z","timestamp":1787336049000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539795285631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":11,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S0097539795285631"],"URL":"https:\/\/doi.org\/10.1137\/s0097539795285631","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}