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Counterexamples to the long-standing conjecture on the complexity of BDD binary operations. (English) Zbl 1248.68265
Summary: In this article, we disprove the long-standing conjecture, proposed by R. E. Bryant in [IEEE Trans. Comput. 35, 677–691 (1986; Zbl 0593.94022)], that his binary decision diagram (BDD) algorithm computes any binary operation on two Boolean functions in linear time in the input-output sizes. We present Boolean functions for which the time required by Bryant’s algorithm is a quadratic of the input-output sizes for all nontrivial binary operations, such as $$\land$$, $$\lor$$, and $$\oplus$$. For the operations $$\land$$ and $$\lor$$, we show an even stronger counterexample where the output BDD size is constant, but the computation time is still a quadratic of the input BDD size. In addition, we present experimental results to support our theoretical observations.

##### MSC:
 68Q25 Analysis of algorithms and problem complexity 68P05 Data structures 68W40 Analysis of algorithms 06E30 Boolean functions 68R10 Graph theory (including graph drawing) in computer science
CUDD
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##### References:
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