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Titlebook: Exploring RANDOMNESS; Gregory J. Chaitin Book 2001 Springer-Verlag London 2001 LISP.Randomness.Ringe.Turing machine.algorithms.complexity.

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發(fā)表于 2025-3-21 17:10:17 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Exploring RANDOMNESS
編輯Gregory J. Chaitin
視頻videohttp://file.papertrans.cn/321/320362/320362.mp4
叢書名稱Discrete Mathematics and Theoretical Computer Science
圖書封面Titlebook: Exploring RANDOMNESS;  Gregory J. Chaitin Book 2001 Springer-Verlag London 2001 LISP.Randomness.Ringe.Turing machine.algorithms.complexity.
描述In The Unknowable I use LISP to compare my work on incompleteness with that of G6del and Turing, and in The Limits of Mathematics I use LISP to discuss my work on incompleteness in more detail. In this book we‘ll use LISP to explore my theory of randomness, called algorithmic information theory (AIT). And when I say "explore" I mean it! This book is full of exercises for the reader, ranging from the mathematical equivalent oftrivial "fin- ger warm-ups" for pianists, to substantial programming projects, to questions I can formulate precisely but don‘t know how to answer, to questions that I don‘t even know how to formulate precisely! I really want you to follow my example and hike offinto the wilder- ness and explore AIT on your own! You can stay on the trails that I‘ve blazed and explore the well-known part of AIT, or you can go off on your own and become a fellow researcher, a colleague of mine! One way or another, the goal of this book is to make you into a participant, not a passive observer of AlT. In other words, it‘s too easy to just listen to a recording of AIT, that‘s not the way to learn music.
出版日期Book 2001
關(guān)鍵詞LISP; Randomness; Ringe; Turing machine; algorithms; complexity; logic; sets; algorithm analysis and problem
版次1
doihttps://doi.org/10.1007/978-1-4471-0307-3
isbn_softcover978-1-4471-1085-9
isbn_ebook978-1-4471-0307-3
copyrightSpringer-Verlag London 2001
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發(fā)表于 2025-3-21 23:45:44 | 只看該作者
https://doi.org/10.1007/978-1-4684-1887-3s in these proofs running on the computer. And in order to write these programs, we need to use a programming language. Unfortunately, no existing programming language is exactly what is needed. So I invented a dialect of LISP that will do the job. In this chapter I’ll explain the version of LISP th
板凳
發(fā)表于 2025-3-22 02:52:01 | 只看該作者
Bond Properties of Self-Compacting Concrete,put graphs. This is our most basic tool. We’ll use it many times: over and over again in what’s left of Part II and in Part III. In fact, using this technique is at the heart of the next two chapters, it’s really what these two chapters are about.
地板
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發(fā)表于 2025-3-22 14:56:31 | 只看該作者
Myoung-Woon Moon,Chansoo Kim,Ashkan Vaziridefinition of a random real. The resulting definition is, in my opinion, a substantial improvement: it’s much easier to apply. And in the next chapter we’ll be able to use it to show that Ω is strong Chaitin random.
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發(fā)表于 2025-3-23 00:08:34 | 只看該作者
Bond Properties of Self-Compacting Concrete,put graphs. This is our most basic tool. We’ll use it many times: over and over again in what’s left of Part II and in Part III. In fact, using this technique is at the heart of the next two chapters, it’s really what these two chapters are about.
9#
發(fā)表于 2025-3-23 04:41:19 | 只看該作者
Chigbogu Ozoegwu,Peter Eberhardchapter I’ll show you two . definitions of a random real that look very different from my program-size irreducibility definition, but which actually turn out to be equivalent. These are P. Martin-L?f’s and R.M. Solovay’s definitions of a random real, and I’ll start with Martin-L?fs definition, which was proposed before Solovay’s.
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