Related papers: Concept and Definition of Complexity
This introductory paper is structured in the form of an "interview", where the author answers the following questions: Why did you begin working with complex systems? How would you define complexity? What is your favourite aspect/concept of…
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…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
The paper "Is Complexity an Illusion?" (Bennett, 2024) provides a formalism for complexity, learning, inference, and generalization, and introduces a formal definition for a "policy". This reply shows that correct policies do not exist for…
At present, there is a great deal of confusion regarding complexity and its measures (reviews on complexity measures are found in, e.g. Lloyd, 2001 and Shalizi, 2006 and more references therein). Moreover, there is also confusion regarding…
This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…
The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we…
In this paper, we introduce the new concept of state complexity approximation, which is a further development of state complexity estimation. We show that this new concept is useful in both of the following two cases: the exact state…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
The evolution of complexity has been a central theme for Biology and Artificial Life (Bonner, 1988; Bedau et al., 2000). Complexification has been interpreted in different ways: as a process of diversification between evolving units…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
Throughout this article we develop and change the definitions and the ideas in "arXiv:1006.4939", in order to consider the efficiency of functions and complexity time problems. The central idea here is effective enumeration and listing, and…
Complexity is often seen as a inherent negative in information design, with the job of the designer being to reduce or eliminate complexity, and with principles like Tufte's "data-ink ratio" or "chartjunk" to operationalize minimalism and…
This chapter does not deal with specific tools and techniques for managing complex systems, but proposes some basic concepts that help us to think and speak about complexity. We review classical thinking and its intrinsic drawbacks when…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as…
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…
Complex analyticity is generalized to hypercomplex functions, quaternion or octonion, in such a manner that it includes the standard complex definition and does not reduce analytic functions to a trivial class. A brief comparison with other…
This is a very basic introduction to some notions related to logic and complexity.
The concept of {\em complexity} (as a quantity) has been plagued by numerous contradictory and confusing definitions. By explicitly recognising a role for the observer of a system, an observer that attaches meaning to data about the system,…