Hardness of identifying the minimum ordered binary decision diagram

Discrete Applied Mathematics

Volumn 107, Issue 1-3, 2000, Pages 191-201

  Takenaga, Yasuhiko ^a   Yajima, Shuzo ^b  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

^b KANSAI UNIVERSITY   (Japan)

Author keywords

Monotone function; NP completeness; Ordered binary decision diagram (OBDD); PAC learning

Indexed keywords

EID: 0347933123     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00226-7     Document Type: Article

References (16)

1. S.B. Akers, Binary decision diagrams, IEEE Trans. Comput. C-27 (1978) 509-516.
2. B. Bollig, M. Löbbing, M. Sauerhoff, I. Wegener, Complexity theoretical aspects of OFDDs, Proceedings of the IFIP WG 10.5 Workshop on Applications of the Reed-Muller Expansion in Circuit Design, 1995.
3. Bollig B., Wegener I. Improving the variable ordering of OBDDs is NP-complete. IEEE Trans. Comput. 45:1996;993-1002.
4. Bryant R.E. Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. C. 35:1986;677-691.
5. S.C. Chang, M. Marek-Sadowska, BDD representation of incompletely specified function, IWLS'93 Workshop Notes, 1993, P6c-1-6.
6. K. Cho, R.E. Bryant, Test pattern generation for sequential CMOS circuits by symbolic fault simulation, Proceedings of the 26th ACM / IEEE DAC, 1989, pp. 418-423.
7. F. Ergün, S.R. Kumar, R. Rubinfeld, On learning bounded-width branching programs, Proceedings of the Eighth COLT, 1995, pp. 361-368.
8. K. Hirata, S. Shimozono, A. Shinohara, On the hardness of approximating the minimum consistent OBDD problem, SWAT'96, Lecture Notes in Computer Science, Vol. 1097, Springer, Berlin, 1996, pp. 112-123.
9. N. Ishiura, Synthesis of multi-level logic circuits from binary decision diagrams, Proceedings of the Synthesis and Simulation Meeting and International Interchange'92, 1992, pp. 74-83.
10. M. Kearns, M. Li, L. Pitt, L.G. Valiant, On the learnability of Boolean formulae, Proceedings of the 19th STOC, 1987, pp. 285-295.
11. S. Minato, N. Ishiura, S. Yajima, Shared binary decision diagram with attribute edges for dfficient Boolean function manipulation, Proceedings of the 27th ACM / IEEE DAC, 1990, pp. 52-57.
12. Pitt L., Valiant L.G. Computational limitations on learning from examples. J. ACM. 35:1988;965-984.
13. Sauerhoff M., Wegener I. On the complexity of minimizing the OBDD size for incompletely specified functions. IEEE Trans. Comput.-Aided Des. Integrated Circuits Systems. 15:1996;1435-1437.
14. T.R. Shiple, R. Hojati, A.L. Sangiovanni-Vincentelli, R.K. Brayton, Heuristic minimization of BDDs using don't cares, 31st ACM / IEEE DAC, 1994, pp. 225-231.
15. S. Tani, K. Hamaguchi, S. Yajima, The complexity of the optimal variable ordering problems of shared binary decision diagrams, Proceedings of the Fourth International Symposium on Algorithm and Computation, Lecture Note in Computer Science, Vol. 762, Springer, Berlin, 1993, pp. 389-398.
16. Valiant L.G. A Theory of the Learnable. Comm. ACM. 27:1984;1134-1142.