Scaled Dimension and Nonuniform Complexity

Scaled Dimension of Individual Strings

We define a new discrete version of scaled dimension and we find connections between the scaled dimension of a string and its Kolmogorov complexity and predictability. We give a new characterization of constructive scaled dimension by Kolmogorov complexity, and prove a new result about scaled dimension and prediction.

Scaled Dimension and the Berman-Hartmanis Conjecture

In 1977, L. Berman and J. Hartmanis [BH77] conjectured that all polynomialtime many-one complete sets for NP are are pairwise polynomially isomorphic. It was stated as an open problem in [LM99] to resolve this conjecture under the measure hypothesis from quantitative complexity theory. In this paper we study the polynomial-time isomorphism degrees within degm(SAT ) in the context of polynomial ...

Resource - Bounded Dimension , Nonuniform Complexity , and Approximation of MAX 3 SAT

Using Rasch scaled stage scores to validate orders of hierarchical complexity of balance beam task sequences.

These studies examine the relationship between the analytic basis underlying the hierarchies produced by the Model of Hierarchical Complexity and the probabilistic Rasch scales that places both participants and problems along a single hierarchically ordered dimension. A Rasch analysis was performed on data from the balance-beam task series. This yielded scaled stage of performance for each of t...

A note on dimensions of polynomial size circuits

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 p 3 -strong dimension 0. We also show that P/poly i.o. has p 3 -dimension 1/2, p 3 -strong dimension 1. Our results improve previous measure results of Lutz (1992) and dimension results of Hitchcock and Vinodchandran (2004).