Showing papers on "Average-case complexity published in 1969"

A variant of the Kolmogorov concept of complexity

Abstract: Kolmogorov in 1965 proposed two related measures of information content (alternately, measures of complexity) based on the size of a program which when processed by a suitable algorithm (machine) yields the desired object. The main emphasis was placed on a conditional complexity measure. In this paper a simple variation of the (restricted) conditional complexity measure investigated by Martin-Lof is noted because of interesting characteristics not shared by the measures proposed by Kolmogorov. The characteristics suggest situations in which this variant is the most desirable measure to employ. The interpretation of the measure offers some desirable general qualities; also the measure is relatively advantageous when working with entities of low complexity and maintains the important properties of the Kolmogorov conditional complexity measure when concerned with high complexity.

On minimal-program complexity measures

Abstract: Brief consideration is given to some properties of three measures of complexity based on the length of minimal descriptive programs. Although the measures explicitly deal with finite sequences, the complexity of an infinite sequence can be regarded as a function mapping each positive integer n to the complexity of the initial segment of length n. Some properties of a complexity hierarchy of infinite sequences with respect to one of the measures is considered.

On classes of computable functions

Abstract: The complexity closure of a computable function is defined by a set of axioms. The axioms are satisfied by complexity classes that are computation time closed and also by other complexity classes which do not have this property. It is then shown that there exist honest recursive functions whose complexity closure are setwise incomparable. Further that there exist chains of honest recursive functions whose complexity closures are densely ordered under set inclusion.