An asymptotically optimal lower bound on the OBDD size of the middle bit of multiplication for the pairwise ascending variable order

Authors:
Martin Sauerhoff
Affiliations:
Krengelstrasse 9, 44869 Bochum, Germany
Venue:
Discrete Applied Mathematics
Year:
2010

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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 x"0,y"0,...,x"n"-"1,y"n"-"1, requires a size of @W(2^(^6^/^5^)^n). This is asymptotically optimal due to a bound of the same order by Amano and Maruoka (2007) [1].