Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Two lower bounds for branching programs
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The complexity of Boolean functions
The complexity of Boolean functions
Efficient implementation of a BDD package
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
Using BDDs to verify multipliers
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
Boolean matching using generalized Reed-Muller forms
DAC '94 Proceedings of the 31st annual Design Automation Conference
DAC '94 Proceedings of the 31st annual Design Automation Conference
Fast OFDD based minimization of fixed polarity Reed-Muller expressions
EURO-DAC '94 Proceedings of the conference on European design automation
On the relation between BDDs and FDDs
Information and Computation
Dynamic variable ordering for ordered binary decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Logic Synthesis and Optimization
Logic Synthesis and Optimization
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Sympathy: fast exact minimization of fixed polarity Reed-Muller expressions for symmetric functions
EDTC '95 Proceedings of the 1995 European conference on Design and Test
How many decomposition types do we need? [decision diagrams]
EDTC '95 Proceedings of the 1995 European conference on Design and Test
Timing-driven optimization using lookahead logic circuits
Proceedings of the 46th Annual Design Automation Conference
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Ordered Decision Diagrams (ODDs) as a means forthe representation of Boolean functions are used in many applicationsin CAD. Depending on the decomposition type, various classes of ODDshave been defined, among them being the Ordered Binary Decision Diagrams (OBDDs), the Ordered Functional Decision Diagrams (OFDDs) and the Ordered Kronecker Functional Decision Diagrams (OKFDDs).Based on a formalization of the concept decomposition type we first investigate all possible decomposition typesand prove that already OKFDDs, which result from the application ofonly three decomposition types, result in the most general class ofODDs. We then show from a (more) theoretical point of view that thegenerality of OKFDDs is really needed. We prove several exponentialgaps between specific classes of ODDs, e.g. between OKFDDs on the oneside and OBDDs, OFDDs on the other side. Combining these results itfollows that a restriction of the OKFDD concept to subclasses, suchas OBDDs and OFDDs as well, results in families of functions whichlose their efficient representation.