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Gregory John Chaitin

Definition

Gregory John Chaitin (1947) logician, American, creative mathematician of the theory of algorithmic data processing.

Description

Even if the concept of elegance is in the form of germ in the work of Leibniz, it is regarded as formalized only after work of Chaitin. This last in the continuation of research of Gödel but also of Turing, knew to highlight this concept in order to make it operational. To be done, it used the notion of the programs. The definition of Chaitin is as follows: An elegant program is the shortest program required a given exit. The theorem of Chaitin can be stated in the following way: It is in general not possible to determine if a given program is elegant or not. It is shown by the absurdity. Indeed, we consider that there is a program E which can test the elegance of a given program. We then build a program B which takes in entry a natural entirety N and enumerates all the possible programs km No which are longer than N B as a program can make turn the program E on the whole of programs km No than it enumerated until A than it finds a program which is elegant. Then B makes turn this program and produces the same exit as this last. Let us consider the following term then: B must produce a result. It is based on the fact that there is an infinity of elegant programs also if the program E functions like he were defined, then there must find of them one, which has the anticipated result. At present let us activate the program B with the entirety N which is this time equal to the length of B+1. B will produce the same exit then as a program km No, which was declared as elegant by the program E But km No is longer than B also km No cannot be elegant. Thus the program E is not a tester of elegance. What is absurd. In this manner, we see that the formalization of this somewhat abstract concept initially makes it possible to obtain a mathematical result of order

Author

Anwar Hossain

Author Email

anwtele@yahoo.com

References

DBLP: Gregory J. Chaitin

Gregory Chaitin - Wikipedia, the free encyclopedia