An asymptotically optimal lower bound on the OBDD size of the middle bit of multiplication for the pairwise ascending variable order |
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Authors: | Martin Sauerhoff |
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Institution: | Krengelstrasse 9, 44869 Bochum, Germany |
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Abstract: | We prove that each OBDD (ordered binary decision diagram) for the middle bit of n-bit integer multiplication for one of the variable orders which so far achieve the smallest OBDD sizes with respect to asymptotic order of growth, namely the pairwise ascending order x0,y0,…,xn−1,yn−1, requires a size of Ω(2(6/5)n). This is asymptotically optimal due to a bound of the same order by Amano and Maruoka (2007) 1]. |
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Keywords: | Multiplication Middle bit OBDD Lower bound Universal hashing |
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