Resource-Bounded Kolmogorov Complexity Revisited

Resour e-Bounded Kolmogorov Complexity Revisited

The pervasive reach of resource-bounded Kolmogorov complexity in computational complexity theory

We continue an investigation into resource-bounded Kolmogorov complexity [ABK06], which highlights the close connections between circuit complexity and Levin’s time-bounded Kolmogorov complexity measure Kt (and other measures with a similar flavor), and also exploits derandomization techniques to provide new insights regarding Kolmogorov complexity. The Kolmogorov measures that have been introd...

NL-printable sets and nondeterministic Kolmogorov complexity

P-printable sets were defined by Hartmanis and Yesha and have been investigated by several researchers. The analogous notion of Lprintable sets was defined by Fortnow et al; both P-printability and L-printability were shown to be related to notions of resource-bounded Kolmogorov complexity. NL-printability was defined by Jenner and Kirsig, but some basic questions regarding this notion were lef...

On Innnite Sequences (almost) as Easy As

It is known that innnite binary sequences of constant Kolmogorov complexity are exactly the recursive ones. Such a kind of statement no longer holds in the presence of resource bounds. Contrary to what intuition might suggest, there are sequences of constant, polynomial-time bounded Kolmogorov complexity that are not polynomial-time computable. This motivates the study of several resource-bound...

Kolmogorov-Loveland Sets and Advice Complexity Classes

Loveland complexity Loveland (1969) is a variant of Kolmogorov complexity, where it is asked to output separately the bits of the desired string, instead of the string itself. Similarly to the resource-bounded Kolmogorov sets we define Loveland sets. We highlight a structural connection between resource-bounded Loveland sets and some advice complexity classes. This structural connection enables...

Resource bounded symmetry of information revisited

The information contained in a string x about a string y is the difference between the Kolmogorov complexity of y and the conditional Kolmogorov complexity of y given x, i.e., I(x : y) = C(y) − C(y |x). The Kolmogorov–Levin Theorem says that I(x : y) is symmetric up to a small additive term. We investigate if this property also holds for several versions of polynomial time bounded Kolmogorov co...