Titlebook: Information and Randomness; An Algorithmic Persp Cristian S. Calude Textbook 2002Latest edition Springer-Verlag Berlin Heidelberg 2002 Chai

Merited

Program-size,One way to measure the . of some text is to determine the size of the smallest string (code, input) from which it can be reproduced by some computer (decoder, interpreter). This idea has been independently formalized in a number of different ways by Solomonoff, Kolmogorov and Chaitin.

Fierce

Random Strings,In this chapter we will address the question: “What is a random string?” A detailed analysis, at both empirical and formal levels, suggests that the correct question is not “Is . a random string?” but “To what extent is . random?”

優(yōu)雅

Monotonous

Computably Enumerable Random Reals,In this chapter we will introduce and study the class of c.e. random reals. A key result will show that this class coincides with the class of all Chaitin’s Omega Numbers.

CAGE

Applications,This chapter discusses some applications of the main results in AIT. They reflect both the power and the beauty of the theory. This part is not so homogeneous; it is not a conclusion, nor a justification.

笨拙的我

Open Problems,AIT raises a large number of challenging open problems; they are motivated both from the inner structure of the theory and from the inter-reaction of the theory with other subjects.

macabre

Noiseless Coding, and the fastest possible methods for transmitting messages. This is a rather special, but important, problem in classical information theory. We rely mainly on the following two central tools: prefix-free sets and Shannon entropy. Undoubtedly, the prefix-free sets are the easiest codes to construct

有偏見(jiàn)

Computably Enumerable Instantaneous Codes,: the extension of the Kraft condition (see Theorem 2.8) to arbitrary c.e. sets and relativized computation. New formulae, closely analogous to expressions in classical information theory, are derived.

赤字

讓空氣進(jìn)入

in each month the superintendent used to organise recitations instead of the usual lessons. We were sitting in groups, each with a teacher, the boys on one side of the long room, the girls on the other. The little dais at the end where the superintendent stood seemed far away, and the poems were sel