Complexity theory may refer to:
Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence.
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree. The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?".
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations, an ecosystem, a living cell, and, ultimately, for some authors, the entire universe.
A New Kind of Science is a book by Stephen Wolfram, published by his company Wolfram Research under the imprint Wolfram Media in 2002. It contains an empirical and systematic study of computational systems such as cellular automata. Wolfram calls these systems simple programs and argues that the scientific philosophy and methods appropriate for the study of simple programs are relevant to other fields of science.
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation (TOC), formal language theory, the lambda calculus and type theory.
The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.
The Santa Fe Institute (SFI) is an independent, nonprofit theoretical research institute located in Santa Fe, New Mexico, United States and dedicated to the multidisciplinary study of the fundamental principles of complex adaptive systems, including physical, computational, biological, and social systems. The institute is ranked 24th among the world's "Top Science and Technology Think Tanks" and 24th among the world's "Best Transdisciplinary Research Think Tanks" according to the 2020 edition of the Global Go To Think Tank Index Reports, published annually by the University of Pennsylvania.
In sociology, social complexity is a conceptual framework used in the analysis of society. In the sciences, contemporary definitions of complexity are found in systems theory, wherein the phenomenon being studied has many parts and many possible arrangements of the parts; simultaneously, what is complex and what is simple are relative and change in time.
Computational sociology is a branch of sociology that uses computationally intensive methods to analyze and model social phenomena. Using computer simulations, artificial intelligence, complex statistical methods, and analytic approaches like social network analysis, computational sociology develops and tests theories of complex social processes through bottom-up modeling of social interactions.
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes
Computational economics is an interdisciplinary research discipline that combines methods in computational science and economics to solve complex economic problems. This subject encompasses computational modeling of economic systems. Some of these areas are unique, while others established areas of economics by allowing robust data analytics and solutions of problems that would be arduous to research without computers and associated numerical methods.
A complex adaptive system is a system that is complex in that it is a dynamic network of interactions, but the behavior of the ensemble may not be predictable according to the behavior of the components. It is adaptive in that the individual and collective behavior mutate and self-organize corresponding to the change-initiating micro-event or collection of events. It is a "complex macroscopic collection" of relatively "similar and partially connected micro-structures" formed in order to adapt to the changing environment and increase their survivability as a macro-structure. The Complex Adaptive Systems approach builds on replicator dynamics.
Complexity measure / measure of complexity may refer to any measure defined in various branches of complexity theory, specifically:
Complexity theory and organizations, also called complexity strategy or complex adaptive organizations, is the use of the study of complexity systems in the field of strategic management and organizational studies. It draws from research in the natural sciences that examines uncertainty and non-linearity. Complexity theory emphasizes interactions and the accompanying feedback loops that constantly change systems. While it proposes that systems are unpredictable, they are also constrained by order-generating rules.
Complexity is the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe.
Complexity economics is the application of complexity science to the problems of economics. It relaxes several common assumptions in economics, including general equilibrium theory. While it does not reject the existence of an equilibrium, it sees such equilibria as "a special case of nonequilibrium", and as an emergent property resulting from complex interactions between economic agents. The complexity science approach has also been applied to computational economics.
Agent-based computational economics (ACE) is the area of computational economics that studies economic processes, including whole economies, as dynamic systems of interacting agents. As such, it falls in the paradigm of complex adaptive systems. In corresponding agent-based models, the "agents" are "computational objects modeled as interacting according to rules" over space and time, not real people. The rules are formulated to model behavior and social interactions based on incentives and information. Such rules could also be the result of optimization, realized through use of AI methods.
The ARC Centre for Complex Systems (ACCS) was established in 2004 from a consortium of Australian universities, led by the University of Queensland. The objective of ACCS was to conduct basic and applied research in the field of complex systems. It conducted research into both the science and engineering of complex systems. Funding was provided by the Australian Research Council (ARC) and the universities involved. The ACCS was funded under the ARC's Centre of Excellence Scheme until mid-2009, after which industry collaborations and further funding was established to continue to apply the Centre's research.
Noam Nisan is an Israeli computer scientist, a professor of computer science at the Hebrew University of Jerusalem. He is known for his research in computational complexity theory and algorithmic game theory.