An improved branch and bound algorithm for exact BDD minimization

Ordered binary decision diagrams (BDDs) are a data structure for efficient representation and manipulation of Boolean functions. They are frequently used in logic synthesis and formal verification. The size of the BDDs depends on a chosen variable ordering, i.e., the size may vary from linear to exp...

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Veröffentlicht in:IEEE transactions on computer-aided design of integrated circuits and systems Jg. 22; H. 12; S. 1657 - 1663
Hauptverfasser: Ebendt, R., Gunther, W., Drechsler, R.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.12.2003
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Binary decision diagrams
Boolean functions
Computer aided design
Computer science
Construction
Costs
Data structures
Design engineering
Formal verification
Logic
Logic synthesis
Lower bounds
Minimization methods
Optimization
Order disorder
Representations
Runtime
Very large scale integration
ISSN:0278-0070, 1937-4151
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Zusammenfassung:Ordered binary decision diagrams (BDDs) are a data structure for efficient representation and manipulation of Boolean functions. They are frequently used in logic synthesis and formal verification. The size of the BDDs depends on a chosen variable ordering, i.e., the size may vary from linear to exponential, and the problem of Improving the variable ordering is known to be NP-complete. In this paper, we present a new exact branch and bound technique for determining an optimal variable order. In contrast to all previous approaches that only considered one lower bound, our method makes use of a combination of three bounds and, by this, avoids unnecessary computations. The lower bounds are derived by generalization of a lower bound known from very large scale integration design. They allow one to build the BDD either top down or bottom up. Experimental results are given to show the efficiency of our approach.
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ISSN:0278-0070
1937-4151
DOI:10.1109/TCAD.2003.819427