KUIS - 96 - 0002 An Exponential Lower Bound of the Size of OBDDs
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چکیده
The size of the Ordered Binary Decision Diagram (OBDD) which represents a Boolean function greatly depends on the ordering of input variables. In this paper, we show that the size of the OBDD representing n-bits integer division is (2 n=8 ) even if any variable ordering is allowed to minimize the size of the OBDD. We also show that _-OBDDs and ^-OBDDs representing division have the same lower bound (2 n=8 ). These lower bounds are obtained from the relation between the cardinality of a 1-fooling set and the size of _-OBDDs, and the relation between the cardinality of a 0-fooling set and the size of ^-OBDDs.
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تاریخ انتشار 1996