Algorithmic Randomness and Computability
نویسنده
چکیده
We examine some recent work which has made significant progress in out understanding of algorithmic randomness, relative algorithmic randomness and their relationship with algorithmic computability and relative algorithmic computability. Mathematics Subject Classification Primary 68Q30, 68Q15, 03D15, 03D25, 03D28, 03D30.
منابع مشابه
On Elementary Computability-Theoretic Properties of Algorithmic Randomness
In this paper we apply some elementary computability-theoretic notions to algorithmic complexity theory with the aim of understanding the role and extent of computability techniques for algorithmic complexity theory. We study some computability-theoretic properties of two different notions of randomness for finite strings: randomness based on the blank-endmarker complexity measure and Chaitin’s...
متن کاملAlgorithmic randomness and measures of complexity
We survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on (weak) reducibilities that measure (a) the initial segment complexity of reals and (b) the power of reals to compress strings, when they are used as oracles. The results are put into context and several connections are made wi...
متن کاملComputability theory, algorithmic randomness and Turing's anticipation
This article looks at the applications of Turing’s Legacy in computation, particularly to the theory of algorithmic randomness, where classical mathematical concepts such as measure could be made computational. It also traces Turing’s anticipation of this theory in an early manuscript.
متن کاملRandomness in Computability Theory
We discuss some aspects of algorithmic randomness and state some open problems in this area. The rst part is devoted to the question \What is a computably random sequence?" Here we survey some of the approaches to algorithmic randomness and address some questions on these concepts. In the second part we look at the Turing degrees of Martin-LL of random sets. Finally, in the third part we deal w...
متن کاملAlgorithmic Randomness as Foundation of Inductive Reasoning and Artificial Intelligence
This article is a brief personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and philosophy. Intuitively, randomness is a lack of order or predictability. If randomness is the opposite of determinism, then algorithmic randomness is the oppos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006