In algorithmic information theory ( a subfield of computer science ), the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object.

Kolmogorov complexity is also known as " descriptive complexity " ( not to be confused with descriptive complexity theory ), Kolmogorov – Chaitin complexity, algorithmic entropy, or program-size complexity.

The concept and theory of Kolmogorov Complexity is based on a crucial theorem first discovered by Ray Solomonoff, who published it in 1960, describing it in " A Preliminary Report on a General Theory of Inductive Inference " as part of his invention of algorithmic probability.

In the 1990s, Jürgen Schmidhuber described an algorithmic theory of beauty which takes the subjectivity of the observer into account and postulates: among several observations classified as comparable by a given subjective observer, the aesthetically most pleasing one is the one with the shortest description, given the observer ’ s previous knowledge and his particular method for encoding the data.

This is closely related to the principles of algorithmic information theory and minimum description length.

Other software including algorithmic beatmatching is Ableton Live, which allows for realtime music manipulation and deconstruction, or Mixmeister, a DJ Mixset creation tool.

The discipline of computing is the systematic study of algorithmic

In the computer science subfield of algorithmic information theory, a Chaitin constant ( Chaitin omega number ) or halting probability is a real number that informally represents the probability that a randomly constructed program will halt.

Diagram illustrating the position of CAAC in relation to other Generative music SystemsComputer-Aided Algorithmic Composition ( CAAC, pronounced " sea-ack ") is the implementation and use of algorithmic composition techniques in software.

The label algorithmic composition is likewise too broad, particularly in that it does not specify the use of a computer.

This is different from other improvisation methods with computers that use algorithmic composition to generate new music without performing analysis of existing music examples.

The theoretical background of compression is provided by information theory ( which is closely related to algorithmic information theory ) for lossless compression, and by rate – distortion theory for lossy compression.

The process is algorithmic and based on dependencies ( mathematical relations ) that exist among relations ' field types.

The data compression ratio can serve as an measure of the complexity of a data set or signal, in particular it is used to approximate the algorithmic complexity.

An arbitrary PID has much the same " structural properties " of a Euclidean domain ( or, indeed, even of the ring of integers ), but knowing an explicit algorithm for Euclidean division, and thus also for greatest common divisor computation, gives a concreteness which is useful for algorithmic applications.

In particular, files of random data cannot be consistently compressed by any conceivable lossless data compression algorithm: indeed, this result is used to define the concept of randomness in algorithmic complexity theory.

* Computational linguistics – study of linguistic issues in a way that is ' computationally responsible ', i. e., taking careful note of computational consideration of algorithmic specification and computational complexity, so that the linguistic theories devised can be shown to exhibit certain desirable computational properties implementations.

The encoder needs to be algorithmic or adaptive whereas the decoder is ' dumb ' and carries out fixed actions.

The algorithmic information content in a number is, roughly speaking, the length of the shortest computer program that will produce that number as output.

If, for instance, the algorithmic view is taken, then the reals as constructed here are essentially what classically would be called the computable numbers.

Multilinear algebra can be developed in greater generality than for scalars coming from a field, but the theory is then certainly less geometric, and computations more technical and less algorithmic.

In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element.

The related but different uniform word problem for a class K of recursively presented groups is the algorithmic problem of deciding, given as input a presentation P for a group G in the class K and two words in the generators of G, whether the words represent the same element of G. Some authors require the class K to be definable by a recursively enumerable set of presentations.

A former student of George Perle, he is currently a professor of music composition at Princeton University, and in addition to his music is known as a pioneer in the development of computer music languages for algorithmic composition ( see Real-Time Cmix ).

Going back over this ground and analyzing the composition of forces which have created the present scene is one of the tasks undertaken by the Center for the Study of Democratic Institutions, in Santa Barbara.

Just because a tree or other object appears in a certain spot is absolutely no reason to place it in the same position in the painting, unless the position serves the design of the whole composition.

`` Speed in painting a picture is valid only when it imparts spontaneity and crispness, but unless the artist has lots of experience so that he can control rapid execution, he would do well to take these first sketches and soberly reorder their design to achieve a unified composition.

he further reasoned that frequent formulas in epic verse indicate oral composition, and assumed the slightly less likely corollary that oral epic is inclined towards the use of formulas.

Even though the bondage of his verse is not so great as the writing poet can manage, it is still great enough for him often to be seriously impeded unless he has aids to facilitate rapid composition.

-- Glycerinated muscle, in the presence of the physiological agent ( ATP ) responsible for delivering energy to the mechanochemically active proteins of muscle, has been shown to undergo a contraction which is highly sensitive both to temperature and to solvent composition in mixtures of alcohols and water.

Thermal conductivity is directly traceable to the material's porous, air-cell construction which effectively traps air or a gas in the maze of minute bubbles which form its composition.

If the photographically realistic continuity of dreams, however bizarre their combinations, denies that it is purely a composition of the brain, it must be compounded from views of diverse realities, although some of them may never be encountered in what we are pleased to call the real life.

A part of the symphonic composition is also featured in As Good as It Gets, released in 1997.

Argon is notable in that its isotopic composition varies greatly between different locations in the solar system.

The effect of angst is achieved by Shostakovich, Mahler and Berg in compositions of wide dynamic range, at times seemingly spinning out of control ( Mahler ), and atonal music using the twelve-tone row method of composition ( Berg, Schoenberg and others ) to create an angst ridden atmosphere of grotesque sound.

The purpose of the composition is to allow complex dialogue scenes to be played out without changes in camera position.

* Closure: composition of two endomorphisms is another endomorphism.

* Associativity: composition of morphisms is always associative.

The composition is jammed by clashing colors, which is unlike what we've seen in the balanced, natural, and dramatic colors of the High Renaissance.

* If M is some set and S denotes the set of all functions from M to M, then the operation of functional composition on S is associative:

In short, composition of maps is always associative.

's No Lark ," and another composition, " Re: Person I Knew " is a tribute to his producer, Orrin Keepnews.

The composition of resins is highly variable ; each species produces a unique blend of chemicals which can be identified by the use of pyrolysis – gas chromatography – mass spectrometry.

The overall chemical and structural composition is used to divide ambers into five classes.

Its chemical composition makes it difficult to match the amber to its producers – it is most similar to the resins produced by flowering plants ; however, there are no flowering plant fossils until the Cretaceous, and they were not common until the Upper Cretaceous.

Amber is a unique preservational mode, preserving otherwise unfossilizable parts of organisms ; as such it is helpful in the reconstruction of ecosystems as well as organisms ; the chemical composition of the resin, however, is of limited utility in reconstructing the phylogenetic affinity of the resin producer.