On the size of randomized OBDDs and read-once branching programs for k-stable functions

Computational Complexity

Volumn 10, Issue 2, 2001, Pages 155-178

  Sauerhoff, Martin ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Communication complexity; Lower bounds; OBDD; Randomness; Read once branching program; Zero error

Indexed keywords

EID: 0035562605     PISSN: 10163328     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00037-001-8193-z     Document Type: Article

References (39)

1. F. ABLAYEV (1996). Lower bounds for one-way probabilistic communication complexity and their application to space complexity. Theoret. Comput. Sci. 157, 139-159.
2. F. ABLAYEV (1997). Randomization and nondeterminism are incomparable for polynomial ordered binary decision diagrams. In Proc. 24th ICALP, Lecture Notes in Comput. Sci. 1256, Springer, 195-202.
3. F. ABLAYEV & M. KARPINSKI (1996). On the power of randomized branching programs. In Proc. 23rd ICALP, Lecture Notes in Comput. Sci. 1099, Springer, 348-356.
4. F. ABLAYEV & M. KARPINSKI (1998). On the power of randomized ordered branching programs. Technical Report 4, Electr. Colloq. on Comput. Complexity.
5. F. ABLAYEV & M. KARPINSKI (1999). A lower bound for integer multiplication on randomized ordered read-once branching programs. In CSIT '99, electronic edition.
6. M. AGRAWAL & T. THIERAUF (1998). The satisfiability problem for probabilistic ordered branching programs. In Proc. 13th IEEE Internat. Conf. on Computational Complexity, 81-90.
7. L. BABAI, P. FRANKL & J. SIMON (1986). Complexity classes in communication complexity theory. In Proc. 27th FOCS, 337-347.
8. L. BABAI, N. NISAN & M. SZEGEDY (1992). Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. System Sci. 45, 204-232.
9. B. BOLLIG, M. SAUERHOFF, D. SIELING & I. WEGENER (1998). Hierarchy theorems for kOBDDs and kIBDDs. Theoret. Comput. Sci. 205, 45-60.
10. B. BOLLIG & I. WEGENER (1999). Complexity theoretical results on partitioned (nondeterministic) binary decision diagrams. Theory Comput. Syst. 32, 487-503.
11. Y. BREITBART, H. B. HUNT III & D. J. ROSENKRANTZ (1995). On the size of binary decision diagrams representing Boolean functions. Theoret. Comput. Sci. 145, 45-69.
12. R. E. BRYANT (1986). Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. C-35, 677-691.
13. R. E. BRYANT (1991). On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication. IEEE Trans. Comput. C-40, 205-213.
14. B. CHOR & O. GOLDREICH (1988). Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput. 17, 230-261.
15. P. E. DUNNE (1984). Lower bounds on the complexity of 1-time only branching programs. In Proc. FCT, Lecture Notes in Comput. Sci. 199, Springer, 90-99.
16. P. ĎURIŠ, J. HROMKOVIČ, J. D. P. ROLIM & G. SCHNITGER (1997). Las Vegas versus determinism for one-way communication complexity, finite automata, and polynomial-time computations. In Proc. 14th STAGS, Lecture Notes in Comput. Sci. 1200, Springer, 117-128.
17. J. FORSTER (2001). A linear lower bound on the unbounded error probabilistic communication complexity. In Proc. IEEE Internat. Conf. on Computational Complexity, to appear.
18. J. GERGOV (1994). Time-space tradeoffs for integer multiplication on various types of input oblivious sequential machines. Inform. Process. Lett. 51, 265-269.
19. J. HROMKOVIČ (1997). Communication Complexity and Parallel Computing. EATCS Texts in Theoretical Computer Science, Springer, Berlin.
20. J. HROMKOVIČ (1998). Communication complexity and lower bounds on multilective computations. In Proc. 23rd MFCS, Lecture Notes in Comput. Sci. 1450, Springer, 789-797.
21. J. HROMKOVIČ & G. SCHNITGER (2001). On the power of Las Vegas for one-way communication complexity, OBDDs, and finite automata. Inform. and Comput. 169, 294-296.
22. J. JAIN, J. BITNER, M. S. ABADIR, J. A. ABRAHAM & D. S. FUSSELL (1997). Indexed BDDs: Algorithmic advances in techniques to represent and verify Boolean functions. IEEE Trans. Comput. 46, 1230-1245.
23. S. JUKNA (1987). Lower bounds on communication complexity. Math. Logic Appl. 5, 22-30.
24. S. JUKNA (1988). Entropy of contact circuits and lower bounds on their complexity. Theoret. Comput. Sci. 57, 113-129.
25. S. JUKNA, A. RAZBOROV, P. SAVICKÝ & I. WEGENER (1999). On P versus NP ∩ co-NP for decision trees and read-once branching programs. Comput. Complexity 8, 357-370.
26. B. KALYANASUNDARAM & G. SCHNITGER (1992). The probabilistic communication complexity of set intersection. SIAM J. Comput. 5, 545-557.
27. M. KARPINSKI (1998). On the computation power of randomized branching programs. In Randomized Algorithms, Proc. Internat. Workshop (Brno), 1-12.
28. M. KRAUSE (1988). Exponential lower bounds on the complexity of local and real-time branching programs. J. Inform. Process. Cybernet. 24, 99-110.
29. M. KRAUSE (1991). Lower bounds for depth-restricted branching programs. Inform. and Comput. 91, 1-14.
30. I. KREMER, N. NISAN & D. RON (1999). On randomized one-round communication complexity. Comput. Complexity 8, 21-49.
31. E. KUSHILEVITZ & N. NISAN (1997). Communication Complexity. Cambridge Univ. Press, Cambridge.
32. R. MUBARAKZJANOV (1999). A note on Las Vegas OBDDs. In CSIT'99, electronic edition.
33. A. RAZBOROV (1992). On the distributional complexity of disjointness. Theoret. Comput. Sci. 106, 385-390.
34. M. SAUERHOFF (1997). A lower bound for randomized read-k-times branching programs. Technical Report 19, Electr. Colloq. on Comput. Complexity.
35. M. SAUERHOFF (1998). Lower bounds for randomized read-k-times branching programs. In Proc. 15th STACS, Lecture Notes in Comput. Sci. 1373, Springer, 105-115.
36. D. SIELING & I. WEGENER (1995). Graph driven BDDs - a new data structure for Boolean functions. Theoret. Comput. Sci. 141, 283-310.
37. I. WEGENER (1988). On the complexity of branching programs and decision trees for clique functions. J. Assoc. Comput. Mach. 35, 461-471.
38. I. WEGENER (2000). Branching Programs and Binary Decision Diagrams - Theory and Applications. Monographs on Discrete and Applied Mathematics, SIAM, Philadelphia, PA.
39. A. C. YAO (1979). Some complexity questions related to distributive computing. In Proc. 11th STOC, 209-213.