Abstract
Optimizing the size of Ordered Binary Decision Diagrams is shown to be NP-complete for monotone Boolean functions. The same result for general Boolean functions was obtained by Bollig and Wegener recently.
Supported in part by Scientific Research Grant, Ministry of Education, Japan
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References
N.Alon and R.B.Boppana: The monotone circuit complexity of Boolean functions, Combinatorica 7(1)a, pp.1–22 (1987).
B.Bollig and I.Wegener: Improving the variable ordering of OBDDs Is NP-complete, IEEE Trans. Comput. Vol.45,No.9,pp.993–1002(1996).
R.E.Bryant: Graph-based algorithms for Boolean function manipulation, IEEE Trans. Comput. Vol.C35,N0.8,pp.677–691(1986).
M.R.Garey, D.S.Johnson and L.Stockmeyer: Some simplified NP-complete graph problems, Theoretical Computer Science, Vol.1, pp.237–267(1976).
K.Hosaka, Y.Takenaga, T. Kaneda and S. Yajima: Size of ordered binary decision diagrams representing threshold functions, Theoret. Comput. Sci.180,pp.47–60 (1997).
S.Jukuna, A.Razborov, P.Savicky and I.Wegener: On P versus NP∩co-NP for decision trees and read-once branching problems, Proc.27nd MFCS, pp.319–326 (1997).
M.R.Mercer, R.Kapur and D.E.Ross: Functional approached to generating orderings for efficient symbolic representation, Proc. 29th ACM/IEEE Design Automation Conference, pp.614–619 (1992).
S.Muroga: Threshold logic and its applications, John Wiley & Sons (1971).
C.E.Shannon: The synthesis of two-terminal switching circuits, Bell Systems Tech.J. 28(1),pp.59–98(1949).
S. Tani, K. Hamaguchi and S. Yajima: The complexity of the optimal variable ordering problems of a shared binary decision diagram, IEICE Trans.Inf.& Syst., Vol.E79-D,No.4,pp.271–281(1996).Also, in Proc.ISAAC93.
E. Tardos: The gap between monotone and non-monotone circuit complexity is exponential, Combinatorica, Vol.8,No.1,pp.141–142(1988).
U.Zwick: A 4n lower bound on the combinational complexity of certain symmetric Boolean functions over the basis of unate dyadic Boolean functions, SIAM J. COMPUT., Vol.20,No.3,pp.499–505(1991).
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© 1998 Springer-Verlag Berlin Heidelberg
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Iwama, K., Nozoe, M., Yajima, S. (1998). Optimizing OBDDs is still intractable for monotone functions. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055813
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DOI: https://doi.org/10.1007/BFb0055813
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