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Sophistication (complexity Theory)
In algorithmic information theory, sophistication is a measure of complexity related to algorithmic entropy. When K is the Kolmogorov complexity and ''c'' is a constant, the sophistication of ''x'' can be defined as : \operatorname_c(x) := \inf \. The constant ''c'' is called significance. The ''S'' variable ranges over finite sets. Intuitively, sophistication measures the complexity of a set of which the object is a "generic" member. See also * Logical depth Logical depth is a measure of complexity for individual strings devised by Charles H. Bennett based on the computational complexity of an algorithm that can recreate a given piece of information. It differs from Kolmogorov complexity in that it ... References Further reading * * * External links The First Law of Complexodynamics Measures of complexity {{comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmic Information Theory
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 (as opposed to stochastically generated), such as strings or any other data structure. In other words, it is shown within algorithmic information theory that computational incompressibility "mimics" (except for a constant that only depends on the chosen universal programming language) 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." Besides the formalization of a universal measure for irreducible information content of computably generated objects, some main achievements of AIT were to show that: in fact algorithmic complexity follows (in the self-delimited case) the same inequalities (except for a constant) t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmic Entropy
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) 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 and is a generalization of classical information theory. The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program ''P'' computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger than ''P'''s own len ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Depth
Logical depth is a measure of complexity for individual strings devised by Charles H. Bennett based on the computational complexity of an algorithm that can recreate a given piece of information. It differs from Kolmogorov complexity in that it considers the computation time of the algorithm with nearly minimal length, rather than the length of the minimal algorithm. Formally, in the context of some universal computer U the logical depth of a string x to significance level s is given by \text\, the running time of the fastest program that produces x and is no more than s longer than the minimal program. See also * Effective complexity * Self-dissimilarity * Forecasting complexity Forecasting complexity is a measure of complexity put forward (under the original name of) by the physicist Peter Grassberger. It was later renamed "statistical complexity" by James P. Crutchfield James P. Crutchfield (born 1955) is an American m ... * Sophistication (complexity theory) Referen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
