Abstract
Free Binary Decision Diagrams (FBDDs) are a data structure for the representation and manipulation of Boolean functions. Efficient algorithms for most of the important operations are known if only FBDDs respecting a fixed graph ordering are considered. However, the size of such an FBDD may strongly depend on the chosen graph ordering and efficient algorithms for computing good or optimal graph orderings are not known. In this paper it is shown that the existence of polynomial time approximation schemes for optimizing graph orderings or for minimizing FBDDs implies NP = P, and so such algorithms are quite unlikely to exist.
Supported in part by DFG grant We 1066/8.
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References
Arora, S., Lund, C., Motwani, R., Sudan, M. and Szegedy, M. (1992). Proof verification and hardness of approximation problems. In Proc. of 33rd Symposium on Foundations of Computer Science, 14–23.
Bern, J., Meinel, C. and Slobodová, A. (1996). Some heuristics for generating tree-like FBDD types. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 15, 127–130.
Blum, M., Chandra, A.K. and Wegman, M.N. (1980). Equivalence of free Boolean graphs can be decided probabilistically in polynomial time. Information Processing Letters 10, 80–82.
Bollig, B. and Wegener, I. (1996). Improving the variable ordering of OBDDs is NP-complete. IEEE Transactions on Computers 45, 993–1002.
Bryant, R.E. (1986). Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers 35, 677–691.
Fortune, S., Hopcroft, J. and Schmidt, E.M. (1978). The complexity of equivalence and containment for free single variable program schemes. In Proc. of 5th International Colloquium on Automata, Languages and Programming, LNCS 62, 227–240.
Garey, M.R. and Johnson, D.S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman.
Gergov, J. and Meinel, C. (1994). Efficient Boolean manipulation with OBDD’s can be extended to FBDD’s. IEEE Transactions on Computers 43, 1197–1209.
Günther, W. and Drechsler, R. (1999). Minimization of free BDDs. In Proc. of Asia and South Pacific Design Automation Conference, 323–326.
Papadimitriou, C.H. and Yannakakis, M. (1991). Optimization, approximation, and complexity classes. Journal of Computer and System Sciences 43, 425–440.
Sieling, D. (1998). On the existence of polynomial time approximation schemes for OBDD-minimization (extended abstract). In Proc. of 15th Symposium on Theoretical Aspects of Computer Science, LNCS 1373, 205–215.
Sieling, D. (1998). The nonapproximability of OBDD minimization. ECCC Report TR98-001, Revision 1 (available from www.eccc.uni-trier.de).
Sieling, D. and Wegener, I. (1995). Graph driven BDDs — a new data structure for Boolean functions. Theoretical Computer Science 141, 283–310.
Simon, J. and Szegedy, M. (1993). A new lower bound theorem for read-only-once branching programs and its applications. In Advances in Computational Complexity Theory, Jin-Yi Cai, ed., DIMACS Series in Discrete Mathematics and Theoretical Computer Science 13, American Mathematical Society, 183–193.
Tani, S., Hamaguchi, K. and Yajima, S. (1993). The complexity of the optimal variable ordering problems of shared binary decision diagrams. In Proc. of 4th International Symposium on Algorithms and Computation, LNCS 762, 389–398.
Wegener, I. (1988). On the complexity of branching programs and decision trees for clique functions. Journal of the Association for Computing Machinery 35, 461–471.
Žák, S. (1984). An exponential lower bound for one-time-only branching programs. In Proc. of Mathematical Foundations of Computer Science, LNCS 176, 562–566.
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Sieling, D. (1999). The Complexity of Minimizing FBDDs. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_23
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DOI: https://doi.org/10.1007/3-540-48340-3_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66408-6
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