A practical comparison of methods to assess sum-of-products

Reliability Engineering and System Safety

Volumn 79, Issue 1, 2003, Pages 33-42

  Rauzy, A ^a   Chatelet E ^a   Dutuit, Y ^a   Berenguer C ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

Binary decision diagrams; Pivotal decomposition; Sum of disjoint products

Indexed keywords

ALGORITHMS; ARTIFICIAL INTELLIGENCE; PROBABILITY; RELIABILITY;

BINARY DECISION DIAGRAMS;

COMPUTATIONAL METHODS;

EID: 0037226753     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0951-8320(02)00165-5     Document Type: Article

References (31)

1. Abraham J.A. An improved algorithm for network reliability. IEEE Trans Reliab. R-28:(1):1979;58-61.
2. Bouhoufani T. Contribution à la construction et au traitement des arbres de défaillance. Thèse de doctorate Université Bordeaux I; 1993.
3. Brace K, Rudell R, Bryant R. Efficient implementation of a BDD package. Proceedings of the 27th ACM/IEEE Design Automation Conference. IEEE 0738; 1990. p. 40-5.
4. Bryant R. Graph based algorithms for Boolean function manipulation. IEEE Trans Comput. 35:(8):1986;677-691.
5. Châtelet E., Dutuit Y., Rauzy A., Bouhoufani T. An optimized procedure to generate sums of disjoint products. Reliab Engng Syst Safety. 65:1999;289-294.
6. Cook SA. The complexity of theorem proving procedures. Proceedings of the Third Annual Symposium on Theory of Computing, ACM; 1971. p. 151-8.
7. Chvátal V., Szemerédi E. Many hard examples for resolution. JACM. 35:(4):1988;759-768.
8. Davis M., Logemann G., Loveland D. A machine program for theorem proving. CACM. 5:1962;394-397.
9. Fujita M, Fujisawa H, Kawato N. Evaluation and improvements of Boolean comparison method based on binary decision diagrams. Proceedings of IEEE International Conference on Computer Aided Design, ICCAD'88; 1988. p. 2-5.
10. Heidtmann K.D. Smaller sums of disjoint products by subproduct inversion. IEEE Trans Reliab. 38:1989;305-311.
11. Hooker J.N., Vinay V. Branching rules for satisfiability. J Automat Reason. 15:1995;359-383.
12. KleineBuning H., Lettman L. Proposition logic: deduction and algorithms. 1999;Cambridge University Press, Cambridge. ISBN 0521630177.
13. Kuo S.-Y., Lu S.-K., Yeh F.-M. Determining terminal-pair reliability based on edge expansion diagrams using OBDD. IEEE Trans Reliab. 48:(3):1999;234-246.
14. Locks M.O., Wilson J.M. Note on disjoint products algorithms. IEEE Trans Reliab. 41:(1):1992;81-84.
15. Liu H.H., Yang W.T., Liu C.C. An improved minimizing algorithm for the summation of disjoint products by Shannon's expansion. Microelectr Reliab. 33:(4):1993;599-613.
16. Madre J-C, Coudert O, Fraïssé H, Bouissou M. Application of a new logically complete ATMS to digraph and network-connectivity analysis. Proceedings of the Annual Reliability and Maintainability Symposium, ARMS'94, Annaheim, California; 1994. p. 118-23.
17. Misra K.R. New trends in system reliability evaluation. Fundamental studies in engineering. vol. 16:1993;Elsevier, Amsterdam. ISBN 0-444-816607.
18. Mitchell D, Selman B, Levesque H. Hard and easy distributions of SAT problems. Proceedings of Tenth National Conference on Artificial Intelligence (AAAI'92); 1992.
19. Nikolskaia M, Rauzy A. Heuristics for BDD handling of sum-of-products formulae. In: Lydersen, Hansen, Sandtorv, editors. Proceedings of European Safety and Reliability Association Conference, ESREL'98, Balkerna, Rotterdam. ISBN 90 54 10 966 1; 1998. p. 1459-65.
20. Page L.B., Perry J.E. A practical implementation of the factoring theorem for newtork reliability. IEEE Trans Reliab. 37:1988;259-267.
21. Page L.B., Perry J.E. Reliability of directed network using the factoring theorem. IEEE Trans Reliab. 38:1989;556-562.
22. Rauzy A. Polynomial restrictions of SAT: what can be done with an efficient implementation of the Davis and Putnam's procedure. In: Montanari U, Rossi F, editors. Proceedings of the International Conference on Principle of Constraint Programming, CP'95, volume 976 of LNCS, Springer Verlag; 1995. p. 515-32.
23. Rauzy A. A new methodology to handle Boolean models with loops. IEEE Trans Reliab. 2002;. in press.
24. Rudell R. Dynamic variable ordering for ordered binary decision. Proceedings of IEEE International Conference on Computer Aided Design, ICCAD'93; November 1993. p. 42-7.
25. Raj S., Veeraraghavan M., Trivedi K.S. A survey of efficient reliability computation using disjoint products approach. Networks. 25:1995;147-163.
26. Shier D.R. Network reliability and algebraic structures. 1991;Oxford Science Publications, Oxford.
27. Soh S., Rai S. Experimental results on preprocessing of path in sum of disjoint products technique. IEEE Trans Reliab. 42:(1):1993;24-33.
28. Toda S. On the computational power of PP and ⊕P. Proceedings of Annual IEEE Symposium on Foundations of Computer Science; 1989. p. 514-9.
29. Valiant L.G. The complexity of enumeration and reliability problems. SIAM J Comput. 8:1979;410-421.
30. Valiant L.G. On the complexity of computing the permanent. Theoret Comput Sci. 8:1979;189-201.
31. Wegener I. Branching programs and binary decision diagrams - theory and applications. SIAM Monographs Discrete Math Appl. 2000;. ISBN 0-89871-4568-3.