Abstract
We show that the middle bit of the multiplication of two n-bit integers can be computed by an ordered binary decision diagram (OBDD) of size less than 2.8 · 2 6 n / 5 . This improves the previously known upper bound of ( 7 3 ) · 2 4 n / 3 by Woelfel (New Bounds on the OBDD-size of integer multiplication via Universal Hashing, J. Comput. System Sci. 71(4) (2005) 520–534). The experimental results suggest that our exponent of 6 n / 5 is optimal or at least very close to optimal. A general upper bound of O ( 2 3 n / 2 ) on the OBDD size of each output bit of the multiplication is also presented.
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