Related papers: Kolmogorov complexity as a language
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
Two-party one-way quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of…
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…
A novel topological and computational method for 'motion' is described. Motion is constrained by inequalities in terms of Kolmogorov Complexity. Causality is obtained as the output of a high-pass filter, passing through only high values of…
We revisit the fundamentals of Circuit Complexity and the nature of efficient computation from a fresh perspective. We present a framework for understanding Circuit Complexity through the lens of Information Theory with analogies to results…
We consider the problem of inferring the probability distribution associated with a language, given data consisting of an infinite sequence of elements of the languge. We do this under two assumptions on the algorithms concerned: (i) like a…
The main purpose of this article is to describe the taxonomy of computer languages according to the levels of abstraction. There exists so many computer languages because of so many reasons like the evolution of better computer languages…
This work aims at discussing the complexity aspect of software while demonstrating its relationship with security. Complexity is an essential part of software; however, numerous studies indicate that they increase the vulnerability of the…
Normalized information distance (NID) uses the theoretical notion of Kolmogorov complexity, which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program.…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
In 1974 Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let data be finite binary strings and models be finite sets of binary strings. Consider model classes consisting of models of given maximal…
The theoretical limits of 'lossy' data compression algorithms are considered. The complexity of an object as seen by a macroscopic observer is the size of the perceptual code which discards all information that can be lost without altering…
Indexed languages are interesting in computational linguistics because they are the least class of languages in the Chomsky hierarchy that has not been shown not to be adequate to describe the string set of natural language sentences. We…
This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the…
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
The provably asymptotically fastest algorithm within a factor of 5 for formally described problems will be constructed. The main idea is to enumerate all programs provably equivalent to the original problem by enumerating all proofs. The…
We present a non-vacuous definition of compositionality. It is based on the idea of combining the minimum description length principle with the original definition of compositionality (that is, that the meaning of the whole is a function of…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes…
This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and…