相关论文: Complexity analysis for algorithmically simple str…

We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given…

Many iterative algorithms in optimization, computational geometry, computer algebra, and other areas of computer science require repeated computation of some algebraic expression whose input changes slightly from one iteration to the next.…

String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we introduce the joint string complexity as the cardinality of a set of words that are common to both strings.…

With the developments in machine learning, there has been a surge in interest and results focused on algorithms utilizing predictions, not least in online algorithms where most new results incorporate the prediction aspect for concrete…

The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity (QC), and rigorous mathematical proofs of its basic properties. The definition used here is similar to that by Berthiaume, van Dam, and Laplante. It…

We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness…

In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…

We present progress on the experimental validation of a fundamental and universally applicable vulnerability analysis framework that is capable of identifying new types of vulnerabilities before attackers innovate attacks. This new…

Classical versions of Kolmogorov complexity are incomputable. Nevertheless, in 1975 Solovay showed that there are computable functions $f > K+O(1)$ such that for infinitely many strings $\sigma$, $f(\sigma)=K(\sigma)+O(1)$, where $K$…

We study the possibility of scaling down algorithmic information quantities in tuples of correlated strings. In particular, we address a question raised by Alexander Shen: whether, for any triple of strings $(a, b, c)$, there exists a…

Although procedural generation is popular among game developers, academic research on the topic has primarily focused on new applications, with some research into empirical analysis. In this paper we relate theoretical work in information…

The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms…

In this paper, we present a theoretical effort to connect the theory of program size to psychology by implementing a concrete language of thought with Turing-computable Kolmogorov complexity (LT^2C^2) satisfying the following requirements:…

We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low…

We study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling with O(n) Kolmogorov complexity of its n-by-n squares. We construct tile sets for which this…

We show that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings $x$ and $y$ is equal, up to logarithmic precision, to the length of the longest shared secret key that two parties, one having $x$ and the…

It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…

A fundamental algorithm for selecting ranks from a finite subset of an ordered set is Radix Selection. This algorithm requires the data to be given as strings of symbols over an ordered alphabet, e.g., binary expansions of real numbers. Its…

Muchnik's theorem about simple conditional descriptions states that for all strings $a$ and $b$ there exists a short program $p$ transforming $a$ to $b$ that has the least possible length and is simple conditional on $b$. In this paper we…

A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…