Related papers: Complexity analysis for algorithmically simple str…
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…
Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…
Kolmogorov complexity theory is used to tell what the algorithmic informational content of a string is. It is defined as the length of the shortest program that describes the string. We present a programming language that can be used to…
Kolmogorov complexity measures the algorithmic complexity of a finite binary string $\sigma$ in terms of the length of the shortest description $\sigma^*$ of $\sigma$. Traditionally, the length of a string is taken to measure the amount of…
Is it possible to find a shortest description for a binary string? The well-known answer is "no, Kolmogorov complexity is not computable." Faced with this barrier, one might instead seek a short list of candidates which includes a laconic…
In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…
We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…
In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the…
Diverse applications of Kolmogorov complexity to learning [CIKK16], circuit complexity [OPS19], cryptography [LP20], average-case complexity [Hir21], and proof search [Kra22] have been discovered in recent years. Since the running time of…
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…
Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…
We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some…
In this paper, we introduce complexity-aware planning for finite-horizon deterministic finite automata with rewards as outputs, based on Kolmogorov complexity. Kolmogorov complexity is considered since it can detect computational…
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…
We introduce a method for analyzing the complexity of natural language processing tasks, and for predicting the difficulty new NLP tasks. Our complexity measures are derived from the Kolmogorov complexity of a class of automata --- {\it…
Given a set X of finite strings, one interesting question to ask is whether there exists a member of X which is simple conditional to all other members of X. Conditional simplicity is measured by low conditional Kolmogorov complexity. We…
We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing…