Ker-I Ko was among the first people to recognize the importance of resource-bounded Kolmogorov complexity as a tool for better understanding the structure of complexity classes. In this brief informal reminiscence, I review the milieu of the early 1980’s that caused an up-welling of interest in resource-bounded Kolmogorov complexity, and then I discuss some more recent work that sheds additional light on the questions related to Kolmogorov complexity that Ko grappled with in the 1980’s and 1990’s. In particular, I include a detailed discussion of Ko’s work on the question of whether it is NP-hard to determine the time-bounded Kolmogorov complexity of a given string. This problem is closely connected with the Minimum Circuit Size Problem (M...
It is a trivial observation that every decidable set has strings of length n with Kolmogorov complex...
Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything w...
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and ...
AbstractWe continue an investigation into resource-bounded Kolmogorov complexity (Allender et al., 2...
We describe the properties of various notions of time-bounded Kolmogorov complexity and other connec...
AbstractWe continue an investigation into resource-bounded Kolmogorov complexity (Allender et al., 2...
AbstractThis paper completely characterizes the Θkp levels of the polynomial hierarchy in terms of K...
We introduce randomized time-bounded Kolmogorov complexity (rKt), a natural extension of Levin's not...
We introduce randomized time-bounded Kolmogorov complexity (rKt), a natural extension of Levin\u27s ...
. This paper presents one method of using time-bounded Kolmogorov complexity as a measure of the com...
We consider sets of strings with high Kolmogorov complexity, mainly in resource-bounded settings but...
This paper presents one method of using time-bounded Kolmogorov complexity as a measure of the compl...
Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything w...
The term "complexity" has different meanings in different contexts. Computational complexity measure...
The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deals with time-bounded Ko...
It is a trivial observation that every decidable set has strings of length n with Kolmogorov complex...
Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything w...
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and ...
AbstractWe continue an investigation into resource-bounded Kolmogorov complexity (Allender et al., 2...
We describe the properties of various notions of time-bounded Kolmogorov complexity and other connec...
AbstractWe continue an investigation into resource-bounded Kolmogorov complexity (Allender et al., 2...
AbstractThis paper completely characterizes the Θkp levels of the polynomial hierarchy in terms of K...
We introduce randomized time-bounded Kolmogorov complexity (rKt), a natural extension of Levin's not...
We introduce randomized time-bounded Kolmogorov complexity (rKt), a natural extension of Levin\u27s ...
. This paper presents one method of using time-bounded Kolmogorov complexity as a measure of the com...
We consider sets of strings with high Kolmogorov complexity, mainly in resource-bounded settings but...
This paper presents one method of using time-bounded Kolmogorov complexity as a measure of the compl...
Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything w...
The term "complexity" has different meanings in different contexts. Computational complexity measure...
The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deals with time-bounded Ko...
It is a trivial observation that every decidable set has strings of length n with Kolmogorov complex...
Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything w...
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and ...