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
Shared binary decision diagram with attributed edges for efficient Boolean function manipulation
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
Learning Conjunctions of Horn Clauses
Machine Learning - Computational learning theory
Horn approximations of empirical data
Artificial Intelligence
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
Complexity of identification and dualization of positive Boolean functions
Information and Computation
Exact learning Boolean functions via the monotone theory
Information and Computation
Artificial Intelligence
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
Doing two-level logic minimization 100 times faster
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Ordered binary decision diagrams as knowledge-bases
Artificial Intelligence
Optimizing OBDDs Is Still Intractable for Monotone Functions
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Formal Verification of Combinational Circuit
VLSID '97 Proceedings of the Tenth International Conference on VLSI Design: VLSI in Multimedia Applications
Translating between Horn representations and their characteristic models
Journal of Artificial Intelligence Research
Boolean approximation revisited
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
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We consider translation among conjunctive normal forms (CNFs), characteristic models, and ordered binary decision diagrams (OBDDs) of Boolean functions. It is shown in this paper that Horn OBDDs can be translated into their Horn CNFs in polynomial time. As for the opposite direction, the problem can be solved in polynomial time if the ordering of variables in the resulting OBDD is specified as an input. In case that such ordering is not specified and the resulting OBDD must be of minimum size, its decision version becomes NP-complete. Similar results are also obtained for the translation in both directions between characteristic models and OBDDs. We emphasize here that the above results hold on any class of functions having a basis of polynomial size.