Circuits over PP and PL

Journal of Computer and System Sciences

Volumn 60, Issue 2, 2000, Pages 422-441

  Beigel, Richard ^a,b   Fu, Bin ^c  

^a University of Illinois at Chicago   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c Epson Palo Alto Laboratory   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN ALGEBRA; COMPUTATIONAL COMPLEXITY; LOGIC GATES; MATHEMATICAL MODELS; SET THEORY; THEOREM PROVING; TURING MACHINES;

BOOLEAN FORMULA REDUCTIONS; ORACLE GATES;

LOGIC CIRCUITS;

EID: 0033873381     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1999.1676     Document Type: Article

References (25)

1. Allender E., Ogihara M. Relationships among PL, #P, and the determinant. Proc. 9th Ann. IEEE Conf. Structure Complexity Theory. 1994;. p. 267-278.
2. Aspnes J., Beigel R., Furst M., Rudich S. The expressive power of voting polynomials. Proc. 23rd Ann. ACM Symp. Theory Comput. 1991;. p. 402-409.
3. Beigel R. Perceptrons, PP, and the polynomial hierarchy. Proc. 7th Ann. IEEE Conf. Structure Complexity Theory. 1992;. p. 14-19.
4. Beigel R. When do extra majority gates help? polylog(n) majority gates are equivalent to one. Comput. Complexity. 4:1994;314-324.
5. Beigel R., Hemachandra L. A., Wechsung G. Probabilistic polynomial time is closed under parity reductions. Inform. Process. Lett. 37:1991;91-94.
6. Beigel R., Reingold N., Spielman D. PP is closed under intersection. J. Comput. System. Sci. 50:1995;191-202.
7. Borodin A., Cook S., Pippenger N. Parallel computation for well-endowed rings and space bounded probabilistic machines. Inform. and Comput. 58:1983;113-136.
8. Brent R. P. The parallel evaluation of general arithmetic expressions. Assoc. Comput. Mach. 21:1974;201-206.
9. Buss S. Algorithms for boolean formula evaluation and for tree contraction. Clote P., Krajicek J. Arithmetic, Proof Theory and Computational Complexity. 1993;96-115 Clarendon Press, Oxford.
10. Buss S., Cook S., Gupta A., Ramachandran V. An optimal parallel algorithm for formula evaluation. SIAM J. Comput. 21:1992;755-780.
11. Buss S. R. The Boolean formula value problem is in ALOGTIME. Proc. 19th Ann. ACM Symp. Theory Comput. 1987;. p. 123-131.
12. Fenner S., Fortnow L., Kurtz S. Gap-definable counting classes. Proc. 6th Ann. IEEE Conf. Structure Complexity Theory. 1991;IEEE Computer Society Press, Los Alamitos. p. 30-42.
13. Fortnow L., Reingold N. PP is closed under truth-table reductions. Inform. and Comput. 124:1996;1-6.
14. Gill J. Computational complexity of probabilistic Turing machines. SIAM J. Comput. 6:1977;675-695.
15. Gottlob G. NP trees and Carnap's modal logic. Proc. 34th Ann. IEEE Symp. Found. Computer Sci. 1993.
16. H. Jung, On probabilistic time and space, Lecture Notes in Computer Science, Vol. 194, pp. 310-317, Springer-Verlag, Berlin, 1985.
17. Lewis P., Stearns R. E., Hartmanis J. Memory bounds for recognition of context-free and context-sensitive languages. Proceedings 6th Ann. IEEE Symp. on Switching Circuit Theory and Logical Design. 1965;. p. 191-202.
18. k. Proc. 11th Ann. Symp. Theor. Aspects Computer Sci. 1994.
19. Ogihara M. The PL hierarchy collapses. Proc. 37th Ann. IEEE Symp. Found. Computer Sci. 1996.
20. Russo D. A. Structural Properties of Complexity Classes. Mar. 1985;Univ. California, Santa Barbara.
21. Ruzzo W., Simon J., Tompa M. Space-bounded hierarchies and probabilistic computations. J. Comput. System Sci. 28:1982;216-230.
22. Simon J. On Some Central Problems Computational Complexity. 1975;Cornell Univ.Dept. Computer Sci., TR 75-224, Ithaca.
23. Spira P. M. On time hardware complexity tradeoffs for boolean functions. Proceedings 4th Hawaii International Symposium on System Sciences. 1971;. p. 525-527.
24. Toda S. PP is as hard as the polynomial-time hierarchy. SIAM J. Comput. 20:1991;865-877.
25. Wilson C. B. Relativized circuit complexity. J. Comput. System Sci. 31:1985;169-181.