Optimal ordered binary decision diagrams for read-once formulas

Discrete Applied Mathematics

Volumn 103, Issue 1-3, 2000, Pages 237-258

  Sauerhoff, Martin ^a   Wegener, Ingo ^a   Werchner, Ralph ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Boolean function; Efficient algorithms; Ordered binary decision diagram; Read once formula; Variable ordering

Indexed keywords

EID: 0037692133     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00210-3     Document Type: Article

References (28)

1. Angluin D., Hellerstein L., Karpinski M. Learning read-once formulas with queries. J. ACM. 40:1993;185-210.
2. B. Bollig, M. Löbbing, I. Wegener, Simulated annealing to improve variable orderings for OBDDs. International Workshop on Logic Synthesis (IWLS), 5/1-5/10, May 1995.
3. Bollig B., Wegener I. Improving the variable ordering of OBDDs is NP-complete. IEEE Trans. Comput. 45(9):1996;993-1002.
4. Bryant R.E. Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. C-35(8):1986;677-691.
5. Bryant R.E. Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Comput. Surveys. 24(3):1992;293-318.
6. Bshouty N.H., Hancock T.R., Hellerstein L. Learning Boolean read-once formulas over generalized bases. J. Comput. System Sci. 50:1995;521-542.
7. K.M. Butler, D.E. Ross, R. Kapur, M.R. Mercer, Heuristics to compute variable orderings for efficient manipulation of ordered binary decision diagrams, Proceedings of the 28th ACM/IEEE Design Automation Conference (DAC), 1991, pp. 417-420.
8. H. Fujii, G. Ootomo, C. Hori, Interleaving based variable ordering methods for ordered binary decision diagrams, Proceedings of the ACM/IEEE International Conference on Computer Aided Design (ICCAD), 1993, pp. 38-41.
9. M. Fujita, H. Fujisawa, N. Kawato, Evaluation and improvements of Boolean comparison method based on binary decision diagrams, Proceedings of the ACM/IEEE International Conference on Computer Aided Design (ICCAD), 2-5, November 1988.
10. M. Fujita, Y. Matsunaga, T. Kakuda, On variable ordering of binary decision diagrams for the application of multi-level logic synthesis, Proceedings of the European Design Automation Conference (EDAC), 1991, pp. 50-54.
11. R.L. Graham, D.E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1994.
12. Hachtel G.D., Somenzi F. A symbolic algorithm for maximum flow in 0-1-networks. Formal Methods System Des. 10:1997;207-219.
13. Heiman R., Newman I., Wigderson A. On read-once threshold formulae and their randomized decision tree complexity. Theoret. Comput. Sci. 107:1993;63-76.
14. N. Ishiura, H. Sawada, S. Yajima, Minimization of binary decision diagrams based on exchange of variables, Proceedings of the ACM/IEEE International Conference on Computer Aided Design (ICCAD), 1991, pp. 472-475.
15. R. Lidl, H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge University Press, Cambridge, 1994.
16. M. Löbbing, I. Wegener, The number of knight's tours equals 33,439,123,484,294 - counting with binary decision diagrams, Electron. J. Combin. 3(#R5) (1996) 1-4.
17. S. Malik, A.R. Wang, R.K. Brayton, A.L. Sangiovanni-Vincentelli, Logic verification using binary decision diagrams in a logic synthesis environment, Proceedings of the ACM/IEEE International Conference on Computer Aided Design (ICCAD), 6-9, November 1988.
18. M.R. Mercer, R. Kapur, D.E. Ross, Functional approaches to generating orderings for efficient symbolic representations, Proceedings of the 29th ACM/IEEE Design Automation Conference (DAC), 1992, pp. 624-627.
19. S. Minato, N. Ishiura, S. Yajima, Shared binary decision diagram with attributed edges for efficient Boolean function manipulation, Proceedigns of the 27th ACM/IEEE Design Automation Conference (DAC), June 1990, pp. 52-57.
20. S. Panda, F. Somenzi, Who are the variables in your neighborhood, International Workshop on Logic Synthesis (IWLS), 5/11-5/20, May 1995.
21. R.L. Rudell, Dynamic variable ordering for ordered binary decision diagrams, Proceedings of the ACM/IEEE International Conference on Computer Aided Design (ICCAD), November 1993, pp. 42-47.
22. D. Sieling, The nonapproximability of OBDD minimization, Technical Report 663, Universität Dortmund (1998). Submitted to Information and Comput.
23. D. Sieling, On the existence of polynomial time approximation schemes for OBDD minimization, Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science (STACS), Lecture Notes in Computer Science, Vol. 1353, Springer, Berlin, 1998.
24. Sieling D., Wegener I. NC -algorithms for operations on binary decision diagrams Parallel Process. Lett. 3(1):1993;3-12.
25. Sieling D., Wegener I. On the representation of partially symmetric Boolean functions by ordered multiple valued decision diagrams. Multiple Valued Logic. 4:1998;63-96.
26. Wegener I. Optimal decision trees and one-time-only branching programs for symmetric Boolean functions. Inform. and Control. 62(2/3):1984;129-143.
27. Wegener I. Comments on A characterization of binary decision diagrams. IEEE Trans. Comput. 43:1994;383-384.
28. I. Wegener, Branching Programs and Binary Decision Diagrams - Theory and Applications, Monographs on Discrete and Applied Mathematics, SIAM, Philadelphia, PA, to appear.