Journal ArticleDOI
On the Complexity of Finite Sequences
A. Lempel,Jacob Ziv +1 more
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TLDR
A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented, related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated.Abstract:
A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented. The proposed complexity measure is related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated. It is further related to the number of distinct substrings and the rate of their occurrence along the sequence. The derived properties of the proposed measure are discussed and motivated in conjunction with other well-established complexity criteria.read more
Citations
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Book ChapterDOI
Speeding up HMM decoding and training by exploiting sequence repetitions
TL;DR: This work presents a method to speed up the dynamic program algorithms used for solving the HMM decoding and training problems for discrete time-independent HMMs and describes three algorithms based alternatively on byte pair encoding, run length encoding and Lempel-Ziv parsing.
Book ChapterDOI
On the Approximation Ratio of Lempel-Ziv Parsing
TL;DR: Z is proved to be the least number of phrases of a general bidirectional parse of a text, where phrases can be copied from anywhere else in the text, and the bound is tight as a function of n, by exhibiting a string family where z = O(b\log (n/b)), where n is the text length.
Journal ArticleDOI
On-line versus off-line computation in dynamic text compression
TL;DR: On-line and off-line coding in the finite case models situations such as distribution of data on CD-ROM where much time can be spent encoding but decoding must be fast and simple.
Journal ArticleDOI
Semiconductor-laser-based hybrid chaos source and its application in secure key distribution
Zexi Zhao,Mengfan Cheng,Chenkun Luo,Lei Deng,Minming Zhang,Songnian Fu,Ming Tang,Ping Shum,Deming Liu +8 more
TL;DR: An analog-digital hybrid optical chaos source and a corresponding secure key distribution (SKD) scheme are proposed to enhance the robustness of the chaotic semiconductor lasers and reduces the requirement on the processing speed of digital components and simplifies the hybrid system structure markedly.
Journal ArticleDOI
Using Lempel–Ziv Complexity to Assess ECG Signal Quality
TL;DR: It is demonstrated that LZ complexity is sensitive to noise level (especially for HF noise) and can thus be a valuable reference index for the assessment of ECG signal quality.
References
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Journal ArticleDOI
Three approaches to the quantitative definition of information
TL;DR: In this article, three approaches to the quantitative definition of information are presented: information-based, information-aware and information-neutral approaches to quantifying information in the context of information retrieval.
Journal ArticleDOI
The definition of random sequences
TL;DR: It is shown that the random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness and can equivalently be considered as the elements which withstand a certain universal stochasticity test.
Journal ArticleDOI
Process complexity and effective random tests
TL;DR: A variant of the Kolmogorov concept of complexity which yields a common theory of finite and infinite random sequences and some concepts of effective tests which are proved to be equivalent are established.
Journal ArticleDOI
Information-Theoretic Limitations of Formal Systems
TL;DR: An attempt is made to apply information-theoretic computational complexity to meta-mathematics by measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theoremic proofs.