Time-space lower bounds for the polynomial-time hierarchy on randomized machines

SIAM Journal on Computing

Volumn 36, Issue 3, 2006, Pages 563-594

  Diehl, Scott ^a   Van Melkebeek, Dieter ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Polynomial time hierarchy; Randomized algorithms; Satisfiability; Time space lower bounds

Indexed keywords

POLYNOMIAL-TIME HIERARCHY; RANDOMIZED ALGORITHMS; TIME-SPACE LOWER BOUNDS;

BOOLEAN ALGEBRA; COMPUTER SIMULATION; ERROR ANALYSIS; POLYNOMIALS; PROBLEM SOLVING; RANDOM PROCESSES;

MACHINERY;

EID: 34250800420     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/050642228     Document Type: Article

References (24)

1. E. ALLENDER, M. KOUCKY, D. RONNEBURGER, S. ROY, AND V. VINAY, Time-apace tradeoffs in the counting hierarchy, in Proceedings of the 16th IEEE Conference on Computational Complexity, IEEE, Los Alamitos, CA, 2001, pp. 295-302.
2. J. BALCÁZAR, J. DÍAZ, AND J. GABARRÓ, Structural Complexity I, EATCS Monogr. Theoret. Comput. Sci. II, Springer-Verlag, Berlin, 1988.
3. P. BEAME, M. SAKS, X. SUN, AND E. VEE, Time-space trade-off lower bounds for randomized computation of decision problems, J. ACM, 50 (2003), pp. 154-195.
4. L. CARTER AND M. WEGMAN, Universal hash functions, J. Comput. System Sci., 18 (1979), pp. 143-154.
5. A. COHEN AND A. WIGDERSON, Dispersers, deterministic amplification, and weak random sources, in Proceedings of the 30th IEEE Symposium on Foundations of Computer Science, IEEE, Los Alamitos, CA, 1989, pp. 14-19.
6. S. COOK, Short prepositional formulas represent nondeterministic computations, Inform. Process. Lett., 26 (1988), pp. 269-270.
7. S. DIEHL AND D. VAN MELKEBEEK, Time-space lower bounds for the polynomial-time hierarchy on randomized machines, in Proceedings of the 32nd International Colloquium On Automata, Languages and Programming, Springer-Verlag, Berlin, 2005, pp. 982-993.
8. L. FORTNOW, Time-space tradeoffs for satisfiability, J. Comput. System Sci., 60 (2000), pp. 337-353.
9. L. FORTNOW AND D. VAN MELKEBEEK, Time-space tradeoffs for nondeterministic computation, in Proceedings of the 15th IEEE Conference on Computational Complexity, IEEE, Los Alamitos, CA, 2000, pp. 2-13.
10. O. GABBER AND Z. GALIL, Explicit constructions of linear-sized superconcentrators, J. Comput. System Sci., 22 (1981), pp. 407-420.
11. J. VON ZUR GATHEN AND J. GERHARD, Modern Computer Algebra, Cambridge University Press, Cambridge, UK, 2003.
12. F. HENNIE AND R. STEARNS, Two-tape simulation of multitape Turing machines, J. Assoc. Comput. Mach., 13 (1966), pp. 533-546.
13. R. IMPAGLIAZZO AND D. ZUCKERMAN, How to recycle random bits, in Proceedings of the 30th IEEE Symposium on Foundations of Computer Science, IEEE, Los Alamitos, CA, 1989, pp. 248-253.
14. R. KANNAN, Towards separating nondeterminism from determinism, Math. Systems Theory, 17 (1984), pp. 29-45.
15. C. LAUTEMANN, BPP and the polynomial hierarchy, Inform. Process. Lett., 17 (1983), pp. 215-217.
16. J. H. VAN LINT, Introduction to Coding Theory, 3rd ed., Springer-Verlag, Berlin, 1999.
17. R. LIPTON AND A. VIGLAS, On the complexity of SAT, in Proceedings of the 40th IEEE Symposium on Foundations of Computer Science, IEEE, Los Alamitos, CA, 1999, pp. 459-464.
18. G. A. MARGULIS, Explicit construction of concentrators, Problems Inform. Transmission, 9 (1973), pp. 325-332.
19. D. VAN MELKEBEEK, Time-space lower bounds for NP-complete problems, in Current Trends in Theoretical Computer Science, G. Paun, G. Rozenberg, and A. Salomaa, eds., World Scientific, River Edge, NJ, 2004, pp. 265-291.
20. N. NISAN, On read-once vs. multiple access to randomness in logspace, Theoret. Comput. Sci., 107 (1993), pp. 135-144.
21. N. NISAN, RL ⊆ SC, Comput. Complex., 4 (1994), pp. 1-11.
22. C. PAPADIMITRIOU, Computational Complexity, Addison-Wesley, Reading, MA, 1994.
23. E. VIOLA, On Probabilistic Time Versus Alternating Time, Tech. Report TR-05-137, Electronic Colloquium on Computational Complexity, 2005. Available online at http://eccc.hpi-web.de/eccc-reports/2005/TROS-137/index. html.
24. R. WILLIAMS, Better time-space lower bounds for SAT and related problems, in Proceedings of the 20th IEEE Conference on Computational Complexity, IEEE, Los Alamitos, CA, 2005, pp. 40-49.