We are concerned with Kolmogorov complexity of strings produced by non-deterministic algorithms. For this, we consider five classes of non-deterministic description modes : (i) Bounded description modes in which the number of outputs depends on programs, (ii) distributed description modes in which the number of outputs depends on the size of the outputs, (iii) spread description modes in which ...

We take a fresh look at CD complexity, where CD t (x) is the smallest program that distinguishes x from all other strings in time t(jxj). We also look at a CND complexity, a new nondeterministic variant of CD complexity. We show several results relating time-bounded C, CD and CND complexity and their applications to a variety of questions in computational complexity theory including: Showing ho...

The goal of music analysis is to find the most satisfying explanations for musical works. It is proposed that this can best be achieved by attempting to write computer programs that are as short as possible and that generate representations that are as detailed as possible of the music to be explained. The theory of Kolmogorov complexity suggests that the length of such a program can be used as...

We derive the coincidence of Lutz’s constructive dimension and Kolmogorov complexity for sets of infinite strings from Levin’s early result on the existence of an optimal left computable cylindrical semi-measure M via simple calculations.

We survey recent developments related to the Minimum Circuit Size Problem and time-bounded Kolmogorov Complexity.

The problem of Information Assurance is approached from the point of view of Kolmogorov Complexity and Minimum Message Length criteria. Several theoretical results are obtained, possible applications are discussed and a new metric for measuring complexity is introduced. Utilization of Kolmogorov Complexity like metrics as conserved parameters to detect abnormal system behavior is explored. Data...