Abstract
In this paper we present theory and experimental results on Algebraic Decision Diagrams. These diagrams extend BDDs by allowing values from an arbitrary finite domain to be associated with the terminal nodes of the diagram. We present a treatment founded in Boolean algebras and discuss algorithms and results in several areas of application: Matrix multiplication, shortest path algorithms, and direct methods for numerical linear algebra. Although we report an essentially negative result for Gaussian elimination per se, we propose a modified form of ADDs which appears to circumvent the difficulties in some cases. We discuss the relevance of our findings and point to directions for future work.
Similar content being viewed by others
References
A.V. Aho, J.E. Hopcroft, and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison Wesley, 1974.
G. Boole, The Mathematical Analysis of Logic, Macmillan, 1847, Reprinted by B. Blackwell, Oxford, UK, 1951.
K.S. Brace, R. Rudell, and R. Bryant, "Efficient implementation of a BDD package," DAC-27: ACM/IEEE Design Automation Conference, Orlando, FL, June 1990, pp. 40-45.
F.M. Brown, Boolean Reasoning: The Logic of Boolean Equations, Kluwer Academic Publishers, 1990.
R. Bryant, "Graph-Based Algorithms for Boolean function manipulation," IEEE Transactions on Computers, Vol. C-35, No. 8, pp. 79-85, Aug. 1986.
J.R. Burch, E.M. Clarke, K.L. McMillan, and D.L. Dill, "Sequential circuit verification using symbolic model checking," DAC-27: ACM/IEEE Design Automation Conference, Orlando, FL, June 1990, pp. 46-51.
J.R. Burch, E.M. Clarke, and D.E. Long, "Representing circuits more efficiently in symbolic model checking," DAC-28: ACM/IEEE Design Automation Conference, San Francisco, CA, June 1991, pp. 403-407.
H. Cho, G.D. Hachtel, S.W. Jeong, B. Plessier, E. Schwarz, and F. Somenzi, "ATPG aspects of FSM verification," ICCAD-90: IEEE International Conference on Computer Aided Design, Santa Clara, CA, Nov. 1990, pp. 134-137.
H. Cho, G.D. Hachtel, E. Macii, B. Plessier, and F. Somenzi, "Algorithms for approximate FSM traversal," DAC-30: ACM/IEEE Design Automation Conference, Dallas, TX, June 1993, pp. 25-30.
E.M. Clarke, K.L. McMillan, X. Zhao, M. Fujita, and J. Yang, "Spectral transforms for large Boolean functions with applications to technology mapping," DAC-30: ACM/IEEE Design Automation Conference, Dallas, TX, June 1993, pp. 54-60.
E.M. Clarke, M. Fujita, P.C. McGeer, K. McMillan, and J. Yang, "Multi-terminal binary decision diagrams: An efficient data structure for matrix representation," IWLS'93: International Workshop on Logic Synthesis, Lake Tahoe, CA, May 1993, pp. 6a:1-15.
T.H. Cormen, C.E. Leiserson, and R.L. Rivest, An Introduction to Algorithms, McGraw-Hill, 1990.
O. Coudert, C. Berthet, and J.C. Madre, "Verification of sequential machines based on symbolic execution," Automatic Verification Methods for Finite State Systems, Lecture Notes in Computer Science, Vol. 407, pp. 365-373, 1989.
O. Coudert, C. Berthet, and J.C. Madre, "Verification of sequential machines using boolean functional vectors," IFIP International Workshop on Applied Formal Methods for Correct VLSI Design, Leuven, Belgium, Nov. 1989, pp. 111-128.
I.S. Duff, "Harwell Subroutine Library," AERE Report R.8730, Atomic Energy Research Establishment, Oxon, England, 1977.
I.S. Duff, A.M. Erisman, and J.K. Reid, Direct Methods for Sparse Matrices, Clarendon Press, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bahar, R., Frohm, E., Gaona, C. et al. Algebric Decision Diagrams and Their Applications. Formal Methods in System Design 10, 171–206 (1997). https://doi.org/10.1023/A:1008699807402
Issue Date:
DOI: https://doi.org/10.1023/A:1008699807402