Related papers: Musings on generic-case complexity
Measuring a document's complexity level is an open challenge, particularly when one is working on a diverse corpus of documents rather than comparing several documents on a similar topic or working on a language other than English. In this…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
The field of computational complexity is concerned both with the intrinsic hardness of computational problems and with the efficiency of algorithms to solve them. Given such a problem, normally one designs an algorithm to solve it and sets…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
Digital Geometry software should reflect the generality of the underlying mathe- matics: mapping the latter to the former requires genericity. By designing generic solutions, one can effectively reuse digital geometry data structures and…
Explainable AI has garnered considerable attention in recent years, as understanding the reasons behind decisions or predictions made by AI systems is crucial for their successful adoption. Explaining classifiers' behavior is one prominent…
Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…
A good process model is expected not only to reflect the behavior of the process, but also to be as easy to read and understand as possible. Because preferences vary across different applications, numerous measures provide ways to reflect…
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…
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…
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…
We introduce and discuss the notion of monotonicity for the complexity measures of general probability distributions, patterned after the resource theory of quantum entanglement. Then, we explore whether this property is satisfied by the…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, that is probability distributions on…