Descriptive Complexity: Kolmogorov Complexity, Descriptive Complexity Theory, Fagin's Theorem, Query, Bit Predicate, First-Order Reduction, Fo

Chapters: Kolmogorov Complexity, Descriptive Complexity Theory, Fagin's Theorem, Query, Bit Predicate, First-Order Reduction, Fo. Source: Wikipedia. Pages: 32. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: 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, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity. For example, consider the following two strings of length 64, each containing only lowercase letters, numbers, and spaces: abababababababababababababababababababababababababababababababab4c1j5b2p0cv4w1x8rx2y39umgw5q85s7uraqbjfdppa0q7nieieqe9noc4cvafzfThe first string has a short English-language description, namely "ab 32 times," which consists of 11 characters. The second one has no obvious simple description (using the same character set) other than writing down the string itself, which has 64 characters. This image illustrates part of the Mandelbrot set fractal. Simply storing the 24-bit color of each pixel in this image would require 1.62 million bits; but a small computer program can reproduce these 1.62 million bits using the definition of the Mandelbrot set. Thus, the Kolmogorov complexity of the raw file encoding this bitmap is much less than 1.62 million.More formally, the complexity of a string is the length of the string's shortest description in some fixed universal description language. The sensitivity of complexity relative to the choice of description language is discussed below. It can be shown that the Kolmogorov complexity of any string cannot be too much larger than the length of the string itself. Stri...More: http: //booksllc.net/?id=163