A note on dimensions of polynomial size circuits

Theoretical Computer Science

Volumn 359, Issue 1-3, 2006, Pages 176-187

  Gu, Xiaoyang ^a  

^a Iowa State University   (United States)

Author keywords

Circuit complexity; Resource bounded dimension; Resource bounded measures

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

CIRCUIT COMPLEXITY; RESOURCE-BOUNDED DIMENSION; RESOURCE-BOUNDED MEASURES;

COMPUTER CIRCUITS;

EID: 33746325500     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2006.02.022     Document Type: Article

References (18)

1. Allender E. When worlds collide: derandomization, lower bounds, and kolmogorov complexity. Proc. 21st Annu. Conf. Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science Vol. 2245 (2001), Springer, Berlin 1-15
2. E. Allender, H. Buhrman, M. Koucký, D. van Melkebeek, D. Ronneburger, Power from random strings, in: Proc. 43rd Ann. IEEE Symp. Foundations of Computer Science, 2002, pp. 669-678, SIAM J. Comput., to appear.
3. Ambos-Spies K., Terwijn S.A., and Zheng X. Resource bounded randomness and weakly complete problems. Theoret. Comput. Sci. 172 1-2 (1997) 195-207
4. K.B. Athreya, J.M. Hitchcock, J.H. Lutz, E. Mayordomo, Effective strong dimension, algorithmic information, and computational complexity, SIAM J. Comput., to appear, Preliminary version appeared in Proc. 21st Internat. Symp. Theoretical Aspects of Computer Science, 2004, pp. 632-643.
5. Hausdorff F. Dimension und äusseres Mass. Math. Ann. 79 (1919) 157-179
6. Hitchcock J.M., Lutz J.H., and Mayordomo E. Scaled dimension and nonuniform complexity. J. Comput. Syst. Sci. 69 2 (2004) 97-122
7. J.M. Hitchcock, N.V. Vinodchandran, Dimension, entropy rates, and compression, in: Proc. 19th IEEE Conf. Computational Complexity, 2004, pp. 174-183, J. Comput. Syst. Sci., to appear.
8. 2. Theoret. Comput. Sci. 143 1 (1995) 149-158
9. Kannan R. Circuit-size lower bounds and non-reducibility to sparse sets. Inform. and Control 55 (1982) 40-56
10. Lutz J.H. Category and measure in complexity classes. SIAM J. Comput. 19 6 (1990) 1100-1131
11. Lutz J.H. Almost everywhere high nonuniform complexity. J. Comput. Syst. Sci. 44 2 (1992) 220-258
12. Lutz J.H. Dimension in complexity classes. SIAM J. Comput. 32 (2003) 1236-1259
13. Lutz J.H. The dimensions of individual strings and sequences. Inform. and Comput. 187 (2003) 49-79
14. Sholomov L.A. A sequence of complexly computable functions. Mate. Zametki 17 6 (1975) 957-966 English version, pp. 574-579
15. L. Stockmeyer, The complexity of decision problems in automata theory and logic, Ph.D. Thesis, Massachusetts Institute of Technology, July 1974.
16. Stockmeyer L.J., and Meyer A.R. Cosmological lower bound on the circuit complexity of a small problem in logic. J. ACM 49 6 (2002) 753-784
17. Sullivan D. Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups. Acta Math. 153 (1984) 259-277
18. Tricot C. Two definitions of fractional dimension. Math. Proc. Cambridge Philos. Soc. 91 (1982) 57-74