{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T10:35:14Z","timestamp":1791110114820,"version":"4.1.0"},"reference-count":4,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1976,3]]},"abstract":"<jats:p>It is shown that for any set of positive integers $\\{ n_1 ,n_2 , \\cdots ,n_p \\} $, there exists a procedure which computes $\\{ x^{n_1 } ,x^{n_2 } , \\cdots ,x^{n_p } \\} $ for any input x in less than $\\lg N + c\\sum_{i = 1}^P [\\lg n_i \/\\lg \\lg (n_i + 2)]$ multiplications for some constant c, where $N = \\max _i \\{ n_i \\} $. This gives a partial solution to an open problem in Knuth [3, \u00a7 4.6.3, Ex. 32] and generalizes Brauer\u2019s theorem on addition chains.<\/jats:p>","DOI":"10.1137\/0205008","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T05:57:56Z","timestamp":1109224676000},"page":"100-103","source":"Crossref","is-referenced-by-count":107,"title":["On the Evaluation of Powers"],"prefix":"10.1137","volume":"5","author":[{"given":"Andrew Chi-Chih","family":"Yao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1939-07068-7"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.4064\/aa-6-1-77-81"},{"key":"R3","volume-title":"The Art of Computer Programming","author":"Knuth D. E.","year":"1969"},{"key":"R4","unstructured":"A. Sch\u00f6nhage,  Eine untere Schranke f\u00fcr die Lange von Additionsketten,  1974, preprint"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0205008","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:35:29Z","timestamp":1787337329000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0205008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1976,3]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1976,3]]}},"alternative-id":["10.1137\/0205008"],"URL":"https:\/\/doi.org\/10.1137\/0205008","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1976,3]]}}}