Very Simple Chaitin Machines for Concrete AITReportar como inadecuado

 Very Simple Chaitin Machines for Concrete AIT

Very Simple Chaitin Machines for Concrete AIT - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Descargar gratis o leer online en formato PDF el libro: Very Simple Chaitin Machines for Concrete AIT
In 1975, Chaitin introduced his celebrated Omega number, the halting probability of a universal Chaitin machine, a universal Turing machine with a prefix-free domain. The Omega numbers bits are {\em algorithmically random}-there is no reason the bits should be the way they are, if we define ``reason to be a computable explanation smaller than the data itself. Since that time, only {\em two} explicit universal Chaitin machines have been proposed, both by Chaitin himself. Concrete algorithmic information theory involves the study of particular universal Turing machines, about which one can state theorems with specific numerical bounds, rather than include terms like O1. We present several new tiny Chaitin machines those with a prefix-free domain suitable for the study of concrete algorithmic information theory. One of the machines, which we call Keraia, is a binary encoding of lambda calculus based on a curried lambda operator. Source code is included in the appendices. We also give an algorithm for restricting the domain of blank-endmarker machines to a prefix-free domain over an alphabet that does not include the endmarker; this allows one to take many universal Turing machines and construct universal Chaitin machines from them.

Autor: Michael Stay


Documentos relacionados