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A note on dimensions of polynomial size circuits
- Source :
-
Theoretical Computer Science . Aug2006, Vol. 359 Issue 1-3, p176-187. 12p. - Publication Year :
- 2006
-
Abstract
- Abstract: In this paper, we use resource-bounded dimension theory to investigate polynomial size circuits. We show that for every , has ith-order scaled -strong dimension 0. We also show that has -dimension and -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 , Theoret. Comput. Sci. 143(1) (1995) 149–158]. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03043975
- Volume :
- 359
- Issue :
- 1-3
- Database :
- Academic Search Index
- Journal :
- Theoretical Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 21742112
- Full Text :
- https://doi.org/10.1016/j.tcs.2006.02.022