We propose the application of information content to analyze the time and space evolution of some boolean networks, and to give a classification of their state as either solid, jelly, liquid, or gaseous, following the ideas of Kauffman. To these aims both individual nodes and the global network are studied by means of data compression. Some experiments are presented using the compression algori...

The material covered in this thesis falls mainly in two parts. In the first part, which is found in chapter II, the foundations of source coding are considered. A careful introduction to the notion of codes for symbols, blocks and infinite sequences is given. The classical notion of a stationary ergodic source is then introduced as a natural concept arising when assuming limiting statistical co...

Two highly effective families of lossless compression methods were created by Ziv and Lempel. However, these methods are normally ineffective when applied to digitized signals. We have successfully adapted the LZ77 method to take advantage of the repetitive nature of ECG waveforms. In our experiments, the resulting algorithm produces much better compression ratios than competing techniques whil...

Some interesting results on a guessing wiretapper’s performance on a Shannon cipher system are summarized. The performance metrics are exponents of guessing moments and probability of large deviations. Connections with compression and the game of twenty questions are discussed. Asymptotic optimality of guessing attacks based on Lempel-Ziv coding lengths is highlighted.

The connection between text compression and the measure of entropy of a source seems to be well known but poorly documented. We try to partially remedy this situation by showing that the topological entropy is a lower bound for the compression ratio of any compressor. We show that for factorial sources the 1978 version of the Ziv-Lempel compression algorithm achieves this lower bound.

The problem of estimating the number of states of a finite-alphabet, finite-state source is investigated. An estimator is developed that asymptotically attains the minimum probability of underestimating the number of states, among all estimators with a prescribed exponential decay rate of overestimation probability. The proposed estimator relies on the Lempel-Ziv data compression algorithm in a...

De Agostino, S., P-complete problems in data compression, Theoretical Computer Science 127 (1994) 181-186. In this paper we study the parallel computational complexity of some methods for compressing data via textual substitution. We show that the Ziv-Lempel algorithm and two standard variations are P-complete. Hence an efficient parallelization of these algorithms is not possible uqless P = NC.

This paper considers online compression algorithms that use at most polylogarithmic space (plogon). These algorithms correspond to compressors in the data stream model. We study the performance attained by these algorithms and show they are incomparable with both pushdown compressors and the Lempel-Ziv compression algorithm.