Exponential lower bounds on the size of OBDDs representing integer division
An Ordered Binary Decision Diagram (OBDD) is a directed acyclic graph representing a Boolean function. The size of OBDDs largely depends on the variable ordering. In this paper, we show the size of the OBDD representing the i-th bit of the output of n-bit/n-bit integer division is Ω(2 (n-i)/8 ) for any variable ordering. We also show that V-OBDDs, Λ-OBDDs and ⊕-OBDDs representing integer division has the same lower bounds on the size. We develop new methods for proving lower bounds on the size of V-OBDDs, Λ-OBDDs and ⊕-OBDDs.
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