Related papers: Physical Complexity of Symbolic Sequences
We present a method for estimating the complexity of an image based on Bennett's concept of logical depth. Bennett identified logical depth as the appropriate measure of organized complexity, and hence as being better suited to the…
Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…
Complexity is a measure of information content. Crystalline materials are not complex systems because their structures can be represented tersely using the language of crystallography. Disordered materials are also structurally simple if…
We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…
A new complexity measure named as Lattice Complexity is presented for finite symbolic sequences. This measure is based on the symbolic dynamics of one-dimensional iterative maps and Lempel-Ziv Complexity. To make Lattice Complexity…
We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
Infinite sequences are of tremendous theoretical and practical importance, and in the Information Age sequences of 0s and 1s are of particular interest. Over the past century, the field of symbolic dynamics has developed to study sequences…
We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
This work uses the L-system to construct a tree structure for the text sequence and derives its complexity. It serves as a measure of structural complexity of the text. It is applied to anomaly detection in data transmission.
It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. But is it possible to construct a few strings, not longer than the input string, so that most of them have larger complexity? We show that the…
An infinite binary sequence has randomness rate at least $\sigma$ if, for almost every $n$, the Kolmogorov complexity of its prefix of length $n$ is at least $\sigma n$. It is known that for every rational $\sigma \in (0,1)$, on one hand,…
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…