{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T18:56:02Z","timestamp":1784746562822,"version":"3.55.0"},"publisher-location":"Berlin, Heidelberg","reference-count":7,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540510833","type":"print"},{"value":"9783540461524","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1989]]},"DOI":"10.1007\/3-540-51083-4_47","type":"book-chapter","created":{"date-parts":[[2012,2,25]],"date-time":"2012-02-25T20:41:58Z","timestamp":1330202518000},"page":"45-58","source":"Crossref","is-referenced-by-count":19,"title":["The multiplicative complexity of boolean functions"],"prefix":"10.1007","author":[{"given":"C. P.","family":"Schnorr","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2005,6,1]]},"reference":[{"key":"5_CR1","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1137\/0208037","volume":"8","author":"J. Ja' Ja'","year":"1979","unstructured":"J. Ja' Ja' (1979): Optimal evaluation of pairs of bilinear forms. Siam J. Computing 8 (1979), 443\u2013462.","journal-title":"Siam J. Computing"},{"key":"5_CR2","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1137\/0209056","volume":"9","author":"J. Ja' Ja'","year":"1980","unstructured":"J. Ja' Ja' (1980): On the complexity of bilinear forms. Siam J. Computing 9 (1980), 713\u2013728.","journal-title":"Siam J. Computing"},{"key":"5_CR3","unstructured":"R. Mirwald and C.P. Schnorr (1987): The multiplicative complexity of quadratic boolean forms. Symposium on 28th annual Symposium on Foundations of Computer Science, Los Angeles, pp. 141\u2013149."},{"key":"5_CR4","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1002\/malq.19860321912","volume":"32","author":"C.P. Schnorr","year":"1986","unstructured":"C.P. Schnorr (1986): A G\u00f6del theorem on network complexity lower bounds. Zeitschrift f\u00fcr math. Logik und Grundlagen der Mathematik 32 (1986), 377\u2013384.","journal-title":"Zeitschrift f\u00fcr math. Logik und Grundlagen der Mathematik"},{"key":"5_CR5","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0304-3975(80)90074-2","volume":"10","author":"C.P. Schnorr","year":"1980","unstructured":"C.P. Schnorr (1980): A 3n-lower bound on the network complexity of Boolean functions. Theor. Comp. Science 10 (1986), 83\u201392.","journal-title":"Theor. Comp. Science"},{"key":"5_CR6","first-page":"184","volume":"264","author":"V. Strassen","year":"1973","unstructured":"V. Strassen (1973): Vermeidung von Divisionen. Crelles Journal f\u00fcr die reine und angew. Mathematik 264 (1973), 184\u2013202.","journal-title":"Crelles Journal f\u00fcr die reine und angew. Mathematik"},{"key":"5_CR7","volume-title":"Perspectives in Mathematics","author":"V. Strassen","year":"1984","unstructured":"V. Strassen (1984): Algebraische Berechnungskomplexit\u00e4t. In Perspectives in Mathematics, Birkh\u00e4user Verlag, Basel."}],"container-title":["Lecture Notes in Computer Science","Applied Algebra, Algebraic Algorithms and Error-Correcting Codes"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-51083-4_47.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T01:00:43Z","timestamp":1619571643000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-51083-4_47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989]]},"ISBN":["9783540510833","9783540461524"],"references-count":7,"URL":"https:\/\/doi.org\/10.1007\/3-540-51083-4_47","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989]]}}}