| 期刊全称 | Algorithmic Randomness and Complexity | | 影响因子2023 | Rodney G. Downey,Denis R. Hirschfeldt | | 视频video | | | 发行地址 | Authors were awarded the 2016 Shoenfield Prize by the Association for Symbolic Logic for outstanding expository writing in the field of logic.Essential resource for researchers and graduate students i | | 学科分类 | Theory and Applications of Computability | | 图书封面 |  | | 影响因子 | Intuitively, a sequence such as 101010101010101010… does not seem random, whereas 101101011101010100…, obtained using coin tosses, does. How can we reconcile this intuition with the fact that both are statistically equally likely? What does it mean to say that an individual mathematical object such as a real number is random, or to say that one real is more random than another? And what is the relationship between randomness and computational power. The theory of algorithmic randomness uses tools from computability theory and algorithmic information theory to address questions such as these. Much of this theory can be seen as exploring the relationships between three fundamental concepts: relative computability, as measured by notions such as Turing reducibility; information content, as measured by notions such as Kolmogorov complexity; and randomness of individual objects, as first successfully defined by Martin-Löf. Although algorithmic randomness has been studied for several decades, a dramatic upsurge of interest in the area, starting in the late 1990s, has led to significant advances. This is the first comprehensive treatment of this important field, designed to be both a refe | | Pindex | Textbook 2010 |
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发表于 2025-3-21 18:22:57
