The complexity of minimizing and learning OBDDs and FBDDs

Discrete Applied Mathematics

Volumn 122, Issue 1-3, 2002, Pages 263-282

  Sieling, Detlef ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Approximation scheme; Binary decision diagram; Branching program; Nonapproximability; PAC learning

Indexed keywords

EID: 84867930241     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(01)00324-9     Document Type: Article

References (26)

1. S. Arora, C. Lund, R. Motwani, M. Sudan, M. Szegedy, Proof verification and hardness of approximation problems, in: Proceedings of 33rd Symposium on Foundations of Computer Science, 1992, pp. 14-23.
2. J. Bern, C. Meinel, and A. Slobodová Some heuristics for generating tree-like FBDD types IEEE Trans. Comput. Aided Des. Integrated Circuits Systems 15 1996 127 130
3. B. Bollig, and I. Wegener Improving the variable ordering of OBDDs is NP-complete IEEE Trans. Comput. 45 1996 993 1002
4. R.E. Bryant Graph-based algorithms for Boolean function manipulation IEEE Trans. Comput. 35 1986 677 691
5. S. Fortune, J. Hopcroft, E.M. Schmidt, The complexity of equivalence and containment for free single variable program schemes, in: Proceedings of Fifth International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 62, Springer, Berlin, 1978, pp. 227-240.
6. S.J. Friedman, and K.J. Supowit Finding the optimal variable ordering for binary decision diagrams IEEE Trans. Comput. 39 1990 710 713
7. M. Fujita, H. Fujisawa, N. Kawato, Evaluation and improvements of Boolean comparison method based on binary decision diagrams, in: International Conference on Computer-Aided Design, 1988, pp. 2-5.
8. M.R. Garey, and D.S. Johnson Computers and Intractability: A Guide to the Theory of NP-Completeness 1979 W.H. Freeman New York
9. J. Gergov, and C. Meinel Efficient Boolean manipulation with OBDD's can be extended to FBDD's IEEE Trans. Comput. 43 1994 1197 1209
10. W. Günther, R. Drechsler, Minimization of free BDDs, in: Proceedings of Asia and South Pacific Design Automation Conference, 1999, pp. 323-326.
11. S. Malik, A.R. Wang, R.K. Brayton, A. Sangiovanni-Vincentelli, Logic verification using binary decision diagrams in a logic synthesis environment, in: International Conference on Computer-Aided Design, 1988, pp. 6-9.
12. C. Meinel, A. Slobodová, On the complexity of constructing optimal ordered binary decision diagrams, in: Proceedings of 19th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Vol. 841, Springer, Berlin, 1994, pp. 515-524.
13. C.H. Papadimitriou, and M. Yannakakis Optimization, approximation, and complexity classes J. Comput. System Sci. 43 1991 425 440
14. L. Pitt, and L.G. Valiant Computational limitations on learning from examples J. Assoc. Comput. Mac. 35 1988 965 984
15. R. Rudell, Dynamic variable ordering for ordered binary decision diagrams, in: Proceedings of International Conference on Computer-Aided Design, 1993, pp. 42-47.
16. D. Sieling, Algorithmen und untere Schranken für verallgemeinerte OBDDs, Ph.D. Thesis, Universität Dortmund. Shaker, Aachen, 1995 (in German).
17. D. Sieling, On the existence of polynomial time approximation schemes for OBDD-minimization (extended abstract), in: Proceedings of 15th Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 1373, Springer, Berlin, 1998, pp. 205-215.
18. D. Sieling, The nonapproximability of OBDD minimization, Information and Computation 172 (2002) 103-138.
19. D. Sieling, The complexity of minimizing FBDDs (extended abstract), in: Proceedings of 24th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Vol. 1672, Springer, Berlin, 1999, pp. 251-261.
20. D. Sieling, and I. Wegener Graph driven BDDs - a new data structure for Boolean functions Theoret. Comput. Sci. 141 1995 283 310
21. J. Simon, M. Szegedy, A new lower bound theorem for read-only-once branching programs and its applications, in: Jin-Yi Cai (Ed.), Advances in Computational Complexity Theory, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 13, American Mathematical Society, Providence, RI, 1993, pp. 183-193.
22. Y. Takenaga, and S. Yajima Hardness of identifying the minimum ordered binary decision diagram Discrete Appl. Math. 107 2000 191 201
23. S. Tani, K. Hamaguchi, S. Yajima, The complexity of the optimal variable ordering problems of shared binary decision diagrams, in: Proceedings of Fourth International Symposium on Algorithms and Computation, Lecture Notes in Computer Science, Vol. 762, Springer, Berlin, 1993, pp. 389-398.
24. L.G. Valiant A theory of the learnable Comm. ACM 27 1984 1134 1142
25. I. Wegener On the complexity of branching programs and decision trees for clique functions J. Assoc. Comput. Mac. 35 1988 461 461
26. S. Žák, An exponential lower bound for one-time-only branching programs, in: Proceedings of 11th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Vol. 176, Springer, Berlin, 1984, pp. 562-566.