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arXiv · 2608.30664

Upper and lower bounds on the OBDD-width of a special integer multiplication

Tong Qin
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Abstract

We consider the Boolean function ${\rm SMul}_{n-1}^n(\boldsymbol{x},\boldsymbol{y})$, which computes the middle bit of the multiplication of two natural numbers represented as $n$-bit binary strings $\boldsymbol{x}$ and $\boldsymbol{y}$, drawn from a restricted domain. We investigate the width of OBDDs computing ${\rm SMul}_{n-1}^n$. We introduce a combinatorially defined function $s_*(n)$ and show that the width of such OBDDs is $Θ(2^{s_*(n)})$.

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Tong Qin. 2026-08-31. Upper and lower bounds on the OBDD-width of a special integer multiplication. https://arxiv.org/abs/2608.30664

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