Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Finding the optimal variable ordering for binary decision diagrams
DAC '87 Proceedings of the 24th ACM/IEEE Design Automation Conference
Efficient implementation of a BDD package
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
Proving circuit correctness using formal comparison between expected and extracted behaviour
DAC '88 Proceedings of the 25th ACM/IEEE Design Automation Conference
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Functional calculations using ordered partial multidecision diagrams
Functional calculations using ordered partial multidecision diagrams
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
Functional approaches to generating orderings for efficient symbolic representations
DAC '92 Proceedings of the 29th ACM/IEEE Design Automation Conference
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Adaptive variable reordering for symbolic model checking
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
OBDD Minimization Based on Two-Level Representation of Boolean Functions
IEEE Transactions on Computers
Minimization of word-level decision diagrams
Integration, the VLSI Journal
Efficient variable ordering and partial representation algorithm
VLSID '95 Proceedings of the 8th International Conference on VLSI Design
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Symbolic simulation via Ordered Binary Decision Diagrams (OBDDs) is becoming more feasible each year. These representations are often very efficient under an appropriate ordering of the variables of the functions represented. Recently, heuristics for ordering variables have been developed, but due to the nature of heuristics, no single heuristic always produces an appropriate ordering. We develop and analyze a technique for selecting the best of several candidate orderings. Our ordering selection method is fast. Its ranking of an ordering is compared to the actual performance of an ordering during functional (OBDD) calculations in circuits from the ISCAS85 combinational benchmarks. Compared to any previously published single ordering heuristic, our method allows OBDD calculations using less cumulative memory over all six circuits investigated, and also produces over an order of magnitude improvement for one or more of those circuits, over every single heuristic examined.