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In algorithmic information theory, the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963.
Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe. In contrast to some other interpretations, such as the Copenhagen interpretation, the evolution of reality as a whole in MWI is rigidly deterministic. Many-worlds is also called the relative state formulation or the Everett interpretation, after physicist Hugh Everett, who first proposed it in 1957. Bryce DeWitt popularized the formulation and named it many-worlds in the 1970s.
Murray Gell-Mann was an American physicist who received the 1969 Nobel Prize in Physics for his work on the theory of elementary particles. He was the Robert Andrews Millikan Professor of Theoretical Physics Emeritus at the California Institute of Technology, a distinguished fellow and one of the co-founders of the Santa Fe Institute, a professor of physics at the University of New Mexico, and the Presidential Professor of Physics and Medicine at the University of Southern California.
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.
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The down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons and protons of atomic nuclei. It is part of the first generation of matter, has an electric charge of −1/3 e and a bare mass of 4.7+0.5
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Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects, such as strings or any other data structure. In other words, it is shown within algorithmic information theory that computational incompressibility "mimics" the relations or inequalities found in information theory. According to Gregory Chaitin, it is "the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously."
Intuitively, an algorithmically random sequence is a sequence of binary digits that appears random to any algorithm running on a universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet. Random sequences are key objects of study in algorithmic information theory.
Foundations of Physics is a monthly journal "devoted to the conceptual bases and fundamental theories of modern physics and cosmology, emphasizing the logical, methodological, and philosophical premises of modern physical theories and procedures". The journal publishes results and observations based on fundamental questions from all fields of physics, including: quantum mechanics, quantum field theory, special relativity, general relativity, string theory, M-theory, cosmology, thermodynamics, statistical physics, and quantum gravity
Toniann Pitassi is a Canadian and American mathematician and computer scientist specializing in computational complexity theory.
In algorithmic information theory, sophistication is a measure of complexity related to algorithmic entropy.
References
- ↑ Gell-Mann, Murray; Lloyd, Seth (1996). "Information Measures, Effective Complexity, and Total Information". Complexity. 2 (1): 44–52. Bibcode:1996Cmplx...2a..44G. doi:10.1002/(SICI)1099-0526(199609/10)2:1<44::AID-CPLX10>3.0.CO;2-X.
- ↑ Ay, Nihat; Muller, Markus; Szkola, Arleta (2010). "Effective Complexity and Its Relation to Logical Depth". IEEE Transactions on Information Theory. 56 (9): 4593–4607. arXiv: 0810.5663 . doi:10.1109/TIT.2010.2053892. S2CID 2217934.
- ↑ McAllister, James W. (2003). "Effective Complexity as a Measure of Information Content". Philosophy of Science. 70 (2): 302–307. doi:10.1086/375469. S2CID 120267550.