Efficient Oblivious Branching Programs for Threshold and Mod Functions

Journal of Computer and System Sciences

Volumn 55, Issue 3, 1997, Pages 373-384

  Sinha, Rakesh Kumar ^a,b   Thathachar, Jayram S ^a  

^a University of Washington   (United States)

^b The Department of Electrical and Computer Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; SWITCHING NETWORKS; THRESHOLD LOGIC;

BRANCHING PROGRAMS; MOD FUNCTIONS; THRESHOLD FUNCTIONS;

COMPUTER SYSTEMS PROGRAMMING;

EID: 0031338276     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1997.1530     Document Type: Article

References (23)

1. N. Alon and W. Maass, Meanders and their applications in lower bounds arguments, J. Comput. System Sci. 37 (1988), 118-129.
2. 1, J. Comput. System Sci. 38 (1989), 150-164.
3. R. E. Bryant and Y. Chen, "Verification of Arithmetic Functions with Binary Moment Diagrams," Technical report CS-94-160, Carnegie Mellon University, School of Computer Science, 1994.
4. R. Burch, E. M. Clarke, D. E. Long, L. McMillan, and D. L. Dill, Symbolic model checking for sequential circuit verification, IEEE Trans. Comput. Aided Design on Integrated Circuits 13, No. 4 (1994), 401-424.
5. L. Babai, P. Pudlák, V. Rödl, and E. Szemerédi, Lower bounds to the complexity of symmetric Boolean functions, Theor. Comput. Sci. 74 (1190), 313-324.
6. A. Borodin, A. A. Razborov, and R. Smolensky, On lower bounds for read-k times branching programs, Comput. Complexity 3 (1993), 1-18.
7. R. E. Bryant, Symbolic Boolean manipulation with ordered binary decision diagrams, ACM Comput. Surveys 24, No. 3 (1992), 283-316.
8. M. Ben-Or and R. Cleve, Computing algebraic formulas using a constant number of registers, SIAM J. Comput. 21 (1992), 54-58.
9. D. A. Mix Barrington and H. Straubing, Superlinear lower bounds for bounded-with branching programs, J. Comput. System Sci. 50 (1995), 374-381.
10. L. Babai, N. Nisan, and M. Szegedy, Multiparty protocols, pseudorandom generators for logspace and time-space trade-offs, J. Comput. System Sci. 45 (1992), 204-232.
11. K. Chandra, M. L. Furst, and R. J. Lipton, Multi-party protocols, in "Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing" pp. 94-99, Boston, MA, April 1983.
12. J. Cai and R. J. Lipton, Subquadratic simulations of circuits by branching programs, SIAM J. Comput. 23, No. 3 (1994), 563-572.
13. R. Cleve, Towards optimal simulations of formulas by bounded-width programs, Comput. Complexity 1 (1991), 91-105.
14. G. H. Hardy and E. M. Wright, "An Introduction to the Theory of Numbers," 5th ed., Oxford University Press, Oxford, 1979.
15. M. Karchmer and A. Wigderson, On span programs, in "Proceedings, IEEE Structure in Complexity Theory, Eighth Annual Conference," pp. 102-111, San Diego, CA, May 1993.
16. O. B. Lupanov, On the problem of realization of symmetric Boolean functions by contact schemes, Problem. Kibernet. (Problems of Cybernetics) 15 (1965), 85-99. [Russian]
17. E. Nečiporuk, On a Boolean function, Soviet Math. Dokl. 7 (1966), 999-1000.
18. P. Pudlák, A lower bound on complexity of branching programs, in "Proceedings of the 11th MFCT, Lecture Notes in Computer Science," Vol. 176, pp. 480-489, Springer-Verlag, New York/Berlin, 1984.
19. A. A. Razborov, Lower bounds on the size of switching-and-rectifier networks for symmetric Boolean functions, Math. Notes Acad. Sci. USSR 48, No. 6 (1990), 79-91.
20. A. A. Razborov, Lower bounds for deterministic and nondeterministic branching programs, in "Fundamentals of Computations Theory: 8th International Conference, FCT '91, Gosen, Germany, September, 1991, Lecture Notes in Computer Science," Vol. 529, pp. 47-60, Springer-Verlag, New York/Berlin, 1992.
21. J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94.
22. R. K. Sinha, "Some Topics in Parallel Computation and Branching Programs," Ph.D. thesis, CSE Technical Report UW-CSE-95-08-02, University of Washington, 1995.
23. I. Wegener, "The Complexity of Boolean Functions," Series in Computer Science, Wiley-Teubner, New York, 1987.