Gregory John Chaitin is an Argentine-American mathematician and computer scientist. Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to Gödel's incompleteness theorem. He is considered to be one of the founders of what is today known as algorithmic complexity together with Andrei Kolmogorov and Ray Solomonoff. Along with the works of e.g. Solomonoff, Kolmogorov, Martin-Löf, and Leonid Levin, algorithmic information theory became a foundational part of theoretical computer science, information theory, and mathematical logic. It is a common subject in several computer science curricula. Besides computer scientists, Chaitin's work draws attention of many philosophers and mathematicians to fundamental problems in mathematical creativity and digital philosophy.
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. Theoretically a large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.
The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is Turing complete and can simulate a universal constructor or any other Turing machine.
A cellular automaton is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling.
Langton's ant is a two-dimensional Turing machine with a very simple set of rules but complex emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. The idea has been generalized in several different ways, such as turmites which add more colors and more states.
Hypercomputation or super-Turing computation is a set of hypothetical models of computation that can provide outputs that are not Turing-computable. For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that could correctly evaluate every statement in Peano arithmetic.
The Rule 110 cellular automaton is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar to Conway's Game of Life. Like Life, Rule 110 with a particular repeating background pattern is known to be Turing complete. This implies that, in principle, any calculation or computer program can be simulated using this automaton.
Quantum Information Science is a field that combines the principles of quantum mechanics with information theory to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it does not include experimental research and can be confused with a subfield of quantum information science that deals with the processing of quantum information.
A cellular automaton (CA) is Life-like if it meets the following criteria:
Seeds is a cellular automaton in the same family as the Game of Life, initially investigated by Brian Silverman and named by Mirek Wójtowicz. It consists of an infinite two-dimensional grid of cells, each of which may be in one of two states: on or off. Each cell is considered to have eight neighbors, as in Life. In each time step, a cell turns on or is "born" if it was off or "dead" but had exactly two neighbors that were on; all other cells turn off. Thus, in the notation describing the family of cellular automata containing Life, it is described by the rule B2/S.
Generative science is an area of research that explores the natural world and its complex behaviours. It explores ways "to generate apparently unanticipated and infinite behaviour based on deterministic and finite rules and parameters reproducing or resembling the behavior of natural and social phenomena". By modelling such interactions, it can suggest that properties exist in the system that had not been noticed in the real world situation. An example field of study is how unintended consequences arise in social processes.
The following tables list the computational complexity of various algorithms for common mathematical operations.
Cristian Sorin Calude is a Romanian-New Zealand mathematician and computer scientist.
In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form where the variables are interpreted as having real number values, and where is a quantifier-free formula involving equalities and inequalities of real polynomials. A sentence of this form is true if it is possible to find values for all of the variables that, when substituted into formula , make it become true.
Golly is a tool for the simulation of cellular automata. It is free open-source software written by Andrew Trevorrow and Tomas Rokicki; it can be scripted using Lua or Python. It includes a hashlife algorithm that can simulate the behavior of very large structured or repetitive patterns such as Paul Rendell's Life universal Turing machine, and that is fast enough to simulate some patterns for 232 or more time units. It also includes a large library of predefined patterns in Conway's Game of Life and other rules.
William Ian Gasarch is an American computer scientist known for his work in computational complexity theory, computability theory, computational learning theory, and Ramsey theory. He is currently a professor at the University of Maryland Department of Computer Science with an affiliate appointment in Mathematics.
In computational geometry, a polygonalization of a finite set of points in the Euclidean plane is a simple polygon with the given points as its vertices. A polygonalization may also be called a polygonization, simple polygonalization, Hamiltonian polygon, non-crossing Hamiltonian cycle, or crossing-free straight-edge spanning cycle.
Juan Felipe Cucker Farkas is an Uruguayan mathematician and theoretical computer scientist who has done research into the complexity theory of the Blum–Shub–Smale computational model and the complexity of numerical algorithms in linear programming and numerical algebraic geometry.
Assembly theory is a framework developed to quantify the complexity of molecules and objects by assessing the minimal number of steps required to assemble them from fundamental building blocks. Proposed by chemist Lee Cronin and his team, the theory assigns an assembly index to molecules, which serves as a measurable indicator of their structural complexity. This approach allows for experimental verification and has applications in understanding selection processes, evolution, and the identification of biosignatures in astrobiology.
This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.
