A Variant of the Kolmogorov Concept of Complexity

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.