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The paper "Computing sequences with addition chains" by P. Downey, B. Leong and R. Sethi, SIAM JOC, v.10, n.3, 1981 proves that finding a shortest addition sequence (i.e. an addition chain containing a given set of integers) is NP-hard. The paper clearly states that it is an open problem whether finding a shortest addition chain for an integer is NP-complete. Despite this clear statement the paper is often misrepresented. Is there a new result showing the NP-completeness of finding addition chains or is this article misquoting the paper above too? 184.108.40.206 21:24, 9 August 2007 (UTC)
You're right, it is indeed a misquote. The Gordon et al. survey states that "Downey et al.  showed that the problem of finding the shortest addition sequence is NP-complete," which I misread as "addition chain". I'll hunt around for more references and then fix the article(s). —Steven G. Johnson 22:16, 9 August 2007 (UTC)
I fixed it after nearly 2 years and made a concise wording shortest / minimal / optimal, hopefully. Regards, Achim1999 (talk) 15:00, 9 July 2009 (UTC)