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

candle

WAG

连累

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.978-1-4471-1085-9978-1-4471-0307-3

天真

凶兆

How to construct self-delimiting Turing machines: the Kraft inequalityput 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.

显而易见

Theoretical interlude—What is randomness? My definitionscally incompressible or irreducible. More precisely, a member of a set of objects is random if it has the highest complexity that is possible within this set. In other words, the random objects in a set are those that have the highest complexity. Applied to the set of all .-bit strings this gives on

来自于

Proof that Martin-Löf randomness is equivalent to Chaitin randomnesschapter 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-Löf’s and R.M. Solovay’s definitions of a random real, and I’ll start with Martin-Löfs definition, which

synovitis

现代

hazard

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 "fi