Abstract
A binary decision diagram (BDD) is a directed acyclic graph for representing a Boolean function. BDD's are widely used in various areas which require Boolean function manipulation, since BDD's can represent efficiently many of practical Boolean functions and have other desirable properties. However the complexity of constructing BDD's has hardly been researched theoretically. In this paper, we prove that the optimal variable ordering problem of shared BDD's is NP-complete, and touch on the hardness of this problem and related problems of BDD's.
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References
S.B.Akers: Binary Decision Diagrams, IEEE Trans. on Computers, C-27(1978), 509–516.
R.E.Bryant: Graph Based Algorithms for Boolean Function Manipulation, IEEE Trans. on Computers, C-35(1986), 677–691.
O.Coudert, C.Berthet, and J.C.Madre: Verification of Sequential Machines Based on Symbolic Execution, Proceedings of the Workshop on Automatic Verification Methods for Finite State Systems, Grenoble, France(1989).
M.Fujita, H.Fujisawa and N.Kawato: Evaluation and Improvements of Boolean Comparison Method Based on Binary Decision Diagrams, IEEE ICCAD-88(1988), 2–5.
S.J.Friedman and K.J.Supowit: Finding the Optimal Variable Ordering for Binary Decision Diagrams, IEEE Trans. on computers, C-39(1986), 710–713.
M.R.Garey, D.S.Johnson and L.Stockmeyer: Some Simplified NP-complete Graph Problems, Theoretical Computer Science 1(1976), 237–267.
S.Minato, N.Ishiura and S.Yajima: Shared Binary Decision Diagram with Attributed Edges for Efficient Boolean Function Manipulation, Proc. 27th ACM/IEEE DAC(1990), 52–57.
M.R.Mercer, R.Kapur and D.E.Ross: Functional Approaches to Generating Ordering for Efficient Symbolic Representations, Proc. 29th ACM/IEEE DAC(1992), 624–629.
N.Ishiura, H.Sawada and S.Yajima: Minimization of Binary Decision Diagrams Based on Exchanges of Variables, IEEE ICCAD-91(1991), 472–475.
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© 1993 Springer-Verlag Berlin Heidelberg
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Tani, S., Hamaguchi, K., Yajima, S. (1993). The complexity of the optimal variable ordering problems of shared binary decision diagrams. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_270
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DOI: https://doi.org/10.1007/3-540-57568-5_270
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