相关论文: Complexity analysis for algorithmically simple str…
We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts…
We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and $\beta$-expansions. These relationships allow to develop intuitions on the complexity behavior of…
Symmetry of information states that $C(x) + C(y|x) = C(x,y) + O(\log C(x))$. We show that a similar relation for online Kolmogorov complexity does not hold. Let the even (online Kolmogorov) complexity of an n-bitstring $x_1x_2... x_n$ be…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
Analyzing the computational complexity of evolutionary algorithms for binary search spaces has significantly increased their theoretical understanding. With this paper, we start the computational complexity analysis of genetic programming.…
The last theme of Kolmogorov's mathematics research was algorithmic theory of information, now often called Kolmogorov complexity theory. There are only two main publications of Kolmogorov (1965 and 1968-1969) on this topic. So Kolmogorov's…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
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…
In this survey, we explore Andrei Nikolayevich Kolmogorov's seminal work in just one of his many facets: its influence Computer Science especially his viewpoint of what herein we call 'Algorithmic Theory of Informatics.' Can a computer file…
For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random…
We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which…
Computational problems can be classified according to their algorithmic complexity, which is defined based on how the resources needed to solve the problem, e.g. the execution time, scale with the problem size. Many problems in…
This is a short introduction to Kolmogorov Complexity. The interested reader is referred to the text books by Cover & Thomas as well as Li & V\'itanyi, which cover the fields of information theory and Kolmogorov complexity in depth and with…
We initiate the theory of communication complexity of individual inputs held by the agents, rather than worst-case or average-case. We consider total, partial, and partially correct protocols, one-way versus two-way, with and without help…
The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.
A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…
It is discussed and surveyed a numerical method proposed before, that alternative to the usual compression method, provides an approximation to the algorithmic (Kolmogorov) complexity, particularly useful for short strings for which…
Loveland complexity is a variant of Kolmogorov complexity, where it is asked to output separately the bits of the desired string, instead of the string itself. Similarly to the resource-bounded Kolmogorov sets we define Loveland sets. We…
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic…
The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can…