Merited
发表于 2025-3-25 05:27:11
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
发表于 2025-3-25 10:50:40
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?”
优雅
发表于 2025-3-25 13:26:37
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Monotonous
发表于 2025-3-25 16:48:39
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
发表于 2025-3-25 22:02:09
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
发表于 2025-3-26 03:42:11
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
发表于 2025-3-26 04:25:37
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
有偏见
发表于 2025-3-26 11:53:31
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
发表于 2025-3-26 13:21:04
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让空气进入
发表于 2025-3-26 20:39:11
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