Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Efficient implementation of a BDD package
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Asymptotically optimal bounds for OBDDs and the solution of some basic OBDD problems
Journal of Computer and System Sciences
Exact OBDD Bounds for Some Fundamental Functions
Theory of Computing Systems
Counterexamples to the long-standing conjecture on the complexity of BDD binary operations
Information Processing Letters
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In 1986 in his seminal paper Bryant has introduced Ordered Binary Decision Diagrams (OBDDs) as a dynamic data structure for the representation and manipulation of Boolean functions which allow efficient algorithms for important operations like synthesis, the combination of two Boolean functions by a Boolean operator, and equivalence checking. Based on his empirical evaluation he has conjectured that his apply algorithm for the synthesis works in linear time with respect to the input and output size. Recently in 2012, Yoshinaka et al. have presented a counterexample which contradicts this conjecture but their example has the drawback that the chosen variable ordering for the OBDD representation of the input and output is bad. Therefore, they have raised the question whether Bryant@?s conjecture may still stand for reasonable variable orderings. Here, a negative answer is given by presenting a simple counterexample which works for such kind of variable orderings.