Problem
Research questions and friction points this paper is trying to address.
OBDD-width
integer multiplication
Boolean function
middle bit
Upper and lower bounds on the OBDD-width of a special integer multiplication
🤖 AI Summary
研究通过引入组合定义函数s_*(n)，确定了计算特定整数乘法中间位的OBDD的宽度上下界为Θ(2^s_*(n))。
📝 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 $Θ(2^{s_*(n)})$.
Innovation
Methods, ideas, or system contributions that make the work stand out.
OBDD-width
special integer multiplication
s_*(n)
middle bit
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