Complexity analysis reveals asymptotic bounds on the OBDD width of middle-bit integer multiplication, suggesting precise memory requirements for restricted arithmetic circuits.
We consider the Boolean function SMulₙ₋₁ⁿ(x,y), which computes the middle bit of the multiplication of two natural numbers represented as n-bit binary strings x and y, drawn from a restricted domain. We investigate the width of OBDDs computing SMulₙ₋₁ⁿ. We introduce a combinatorially defined function s_*(n) and show that the width of such OBDDs is Θ(2s_*(n)).
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Tong Qin (2026) studied this question.
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