Category and measure in complexity classes
SIAM Journal on Computing
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Theoretical Computer Science
Resource bounded randomness and weakly complete problems
Theoretical Computer Science
Cosmological lower bound on the circuit complexity of a small problem in logic
Journal of the ACM (JACM)
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Dimension in Complexity Classes
SIAM Journal on Computing
The dimensions of individual strings and sequences
Information and Computation
Dimension, Entropy Rates, and Compression
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Scaled dimension and nonuniform complexity
Journal of Computer and System Sciences
Dimension, entropy rates, and compression
Journal of Computer and System Sciences
Theoretical Computer Science
Effective Dimensions and Relative Frequencies
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Resource-bounded strong dimension versus resource-bounded category
Information Processing Letters
Effective dimensions and relative frequencies
Theoretical Computer Science
| Hi-index | 5.23 |
In this paper, we use resource-bounded dimension theory to investigate polynomial size circuits. We show that for every i ≥0, P/poly has ith-order scaled p3-strong dimension 0. We also show that P/polyi.o. has p3-dimension 1/2 and p3-strong dimension 1. Our results improve previous measure results of Lutz [Almost everywhere high nonuniform complexity, J. Comput. Syst. Sci. 44(2) (1992) 220-258] and dimension results of Hitchcock and Vinodchandran [Dimension, entropy rates, and compression, in: Proc. 19th IEEE Conf. Computational Complexity, 2004, pp. 174-183, J. Comput. Syst. Sci., to appear]. Additionally, we establish a Supergale Dilation Theorem, which extends the martingale dilation technique introduced implicitly by Ambos-Spies, Terwijn, and Zheng [Resource bounded randomness and weakly complete problems, Theoret. Comput. Sci. 172(1-2)(1997) 195-207] and made explicit by Juedes and Lutz [Weak completeness in E and E2, Theoret. Comput. Sci. 143(1) (1995) 149-158].