On the Complexity of Finite Sequences

By A. Lempel, J. Ziv. 1976

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Causal Markov condition for submodular information measures (2010, background): “In the original paper of Ziv and Lempel (1976) it was shown that c is subadditive: for two strings x and y the information of the concatenated string xy is at most the information of x plus the information of y.”
Computational Mechanics: Pattern and Prediction, Structure and Simplicity (1999, unknown): “bularies’’ built by universal coding schemes, such as the popular Lempel– Ziv algorithm ( 127 , 128)).”
A Theoretically Based Index of Consciousness Independent of Sensory Processing and Behavior (2013, methodology): “1): (i) recording the brain’s early reaction (within the first 300 ms) to a direct TMS-induced cortical perturbation with high-density electroencephalography (hd-EEG) (25); (ii) performing source modeling and nonparametric statistics to extract a binary matrix of significant sources [SS(x,t)] that d”
Quantifying Neural Correlations Using Lempel-Ziv Complexity (2008, unknown): “In particular, using the implementation of LempelZiv complexity (LZC) [1], one gains the advantage on two finite size issues : an accurate control of the statistical fluctuations (sampling issue) [2] and a better estimation of an asymptotic quantity (convergence issue) [3].”
Analysis of EEG background activity in Alzheimer's disease patients with Lempel-Ziv complexity and central tendency measure. (2006, background): “The LZ complexity [24] is a nonparametric measure of complexity in a onedimensional signal related to the number of distinct substrings and the rate of their recurrence.”
EEG complexity as a measure of depth of anesthesia for patients (2001, methodology): “Suppose the number of different symbols in a symbol set is and the length of sequence is , where denotes the set of all finite length sequences over the finite symbol set . In [ 33 ], it has been proved that the upper bound of is given by”
Grammar-based codes: A new class of universal lossless source codes (2000, methodology): “of , by which we mean the parsing of established in the paper [15] and used in the 1978 version of the Lempel–Ziv data compression algorithm [27].”
Handbook of Applied Cryptography (2018, methodology): “Another complexity measure, the Ziv-Lempel complexity measure, was proposed by Ziv and Lempel [1273].”
Diagnosis of Alzheimer's disease from EEG signals: where are we standing? (2010, background): “, [77]), and Lempel-Ziv complexity [78, 79, 80, 81].”
Indexing Compressed Text (2003, unknown): “Another, somewhat similar proof appears in [11].”
Design and Analysis of Algorithms (2009, unknown): “Utilizing fast algorithms for rectangular matrix multiplication has proved to be quite useful for improving the complexity of solving many of those problems (a very partial list includes [16,25,7,36,27,34,35,23,24]).”
Efficient universal lossless data compression algorithms based on a greedy sequential grammar transform .2. With context models (2000, methodology): “So far, the most widely used universal lossless compression algorithms are arithmetic coding algorithms [1], [20], [22], [23], [29], Lempel–Ziv algorithms [16], [35], [36], and their variants.”
Efficient universal lossless data compression algorithms based on a greedy sequential grammar transform - Part one: Without context models (2000, methodology): “So far, the most widely used universal lossless compression algorithms are arithmetic coding algorithms [1], [20], [22], [23], [29], Lempel–Ziv algorithms [16], [35], [36], and their variants.”
Interpretation of the Lempel-Ziv Complexity Measure in the Context of Biomedical Signal Analysis (2006, background): “This complexity measure is related to the number of distinct substrings (i.e., patterns) and the rate of their occurrence along a given sequence [2].”