Better upper bounds on the QOBDD size of integer multiplication

Authors:
Kazuyuki Amano;Akira Maruoka
Affiliations:
Department of Computer Science, Gunma University, Tenjin 1-5-1, Kiryu, Gunma 376-8515, Japan;Graduate School of Information Sciences, Tohoku University, Aoba 6-6-05, Aramaki, Sendai 980-8579, Japan
Venue:
Discrete Applied Mathematics
Year:
2007

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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 (73).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 6n/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.