The Lempel–Ziv universal coding scheme is asymptotically optimal for the class of all stationary ergodic sources. A problem of robust-ness of this property under small violations of ergodicity is studied. A notion of deficiency of algorithmic randomness is used as a measure of disagreement between data sequence and probability measure. We prove that universal compressing schemes from a large cl...

A new notion of empirical informational divergence (relative entropy) between two individual sequences is introduced. If the two sequences are independent realizations of two finiteorder, finite alphabet, stationary Markov processes, the empirical relative entropy converges to the relative entropy almost surely. This new empirical divergence is based on a version of the Lempel-Ziv data compress...

The Lempel-Ziv codes are universal variable-tofixed length codes that have become virtually standard in practical lossless data compression. For any given source output string from a Markov or unifilar source, we upper-bound the difference between the number of binary digits needed to encode the string and the self-information of the string. We use this result to demonstrate that for unifilar o...

We address the problem of string matching on Ziv-Lempel compressed text. The goal is to search a pattern in a text without un-compressing it. This is a highly relevant issue to keep compressed text databases where eecient searching is still possible. We develop a general technique for string matching when the text comes as a sequence of blocks. This abstracts the essential features of Ziv-Lempe...

-Lossless block-to-variable length source coding is studied for finite-state, finite-alphabet sources. We aim to minimize the probability that the normalized length of the codeword will exceed a given threshold B, subject to the Kraft inequality. It is shown that the Lempel-Ziv (LZ) algorithm asymptotically attains the optimal performance in the sense just defined, independently of the source a...

We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topologi...

The Lempel–Ziv universal coding scheme is asymptotically optimal for the class of all stationary ergodic sources. A problem of robustness of this property under small violations of ergodicity is studied. A notion of deficiency of algorithmic randomness is used as a measure of disagreement between data sequence and probability measure. We prove that universal compressing schemes from a large cla...

In a given binary image, we identify two disjoint sets of image subblocks of varying size which we call range blocks and domain blocks. The range blocks form a partition of the image called a self-referential partition because each range block is represented via a pointer to a matching domain block. The encoder transmits encoded versions of these pointers together with one pixel from each domai...

We present the results of applying lossless and lossy data compression to a three-dimensional object reconstruction and recognition technique based on phase-shift digital holography. We find that the best lossless (Lempel-Ziv, Lempel-Ziv-Welch, Huffman, Burrows-Wheeler) compression rates can be expected when the digital hologram is stored in an intermediate coding of separate data streams for r...

Estimation of distribution algorithm (EDA) can solve more complicated problems than its predecessor (Genetic Algorithm). EDA uses various methods to probabilistically model a group of highly fit individuals. Calculating the model in sophisticated EDA is very time consuming. To reduce the model building time, the authors propose compressed chromosome encoding. A chromosome is encoded using a for...