The C-oscillation due to Martin-Löf shows that {α| ∀ n [C(α n)≥ n-O(1)]=, which also follows {α| ∀ n [K(α n)≥ n+K(n)-O(1)]=. By generalizing them, we show that there does not exist a real α such that ∀ n (K(α n)≥ n+λ K(n)-O(1)) for any λ>0.

Currently, the most popular model in data compression theory is that of stationary ergodic sources. But there do exist sequences each of which is not emitted from any stationary ergodic source but can be compressed sufficiently by a certain algorithm. We estimate the size of the set of such sequences in terms of Hausdorff dimension.

Image classification is an important task in document image analysis and understanding, page segmentation-based document image compression, and image retrieval. In this paper, we present a new approach for distinguishing textual images from pictorial images using the Kolmogorov Complexity (KC) measure with randomly extracted blocks. In this approach, a number of blocks are extracted randomly from a binarized image and each block image is converted into a one-dimensional binary sequence using either horizontal or vertical scanning. The complexities of these blocks are then computed and the mean value and standard deviation of the block complexities are used to classify the image into textual or pictorial image based on two simple fuzzy rules. Experimental results on different textual and pictorial images show that the KC measure with randomly extracted blocks can efficiently classified 29 out 30 images. The performance of our approach, where an explicit training process is not needed, is comparable favorably to that of a neural network-based approach.

K-randomness and Martin-Lof randomness are among many formalizations of randomness of infinite sequences, and these two are known to be equivalent. We can naturally modify the former to the definition of partial randomness. However, it is not obvious how to modify the latter to the definition of partial randomness. In this paper, we show that we can modify Martin-Lof randomness to a definition of partial randomness that is equivalent to the definition obtained by naturally modifying K-randomness. The basic idea is to modify the notion of measures used in the definition of Martin-Lof tests.

In [2] Ibarra introduced a restricted version of one-way multihead pushdown automaton (PDA), called a simple one-way multihead PDA, and showed that such machines recognize only languages with semilinear property. The main result of this paper is that for each k 1, simple (sensing) one-way (k + 1)-head PDA's are more powerful than simple (sensing) one-way k-head PDA's. This paper also investigates closure properties for simple (sensing) one-way multihead PDA's

This paper establishes a relationship among the accepting powers of deterministic, nondeterministic, and alternating one-way auxiliary pushdown automata, for any tape bound below n. Some other related results are also presented.

By a measure we mean a function µ from {0, 1}* (the set of all binary sequences) to real numbers such that µ(x)0 and µ({0, 1}*). A malign measure is a measure such that if an input x in {0, 1}n (the set of all binary sequences of length n) is selected with the probability µ(x)/µ ({0, 1}n) then the worst-case computation time tWOA (n) and the average-case computation time tav,µA(n) of an algorithm A for inputs of length n are functions of n of the same order for any algorithm A. Li and Vitányi found that measures that are known as a priori measures are malign. We prove that a priori" -ness and malignness are different in one strong sense.