Exploring RANDOMNESS by Gregory J. Chaitin

Exploring RANDOMNESS by Gregory J. Chaitin

Author:Gregory J. Chaitin
Language: eng
Format: epub
Publisher: Springer-Verlag Wien 2012
Published: 2015-04-12T16:00:00+00:00


The message of Part II will be that in order to study the properties of this complexity measure, of the size of the smallest program for x, you actually have to look at all the programs that calculate x, you have to look at the probability of getting x at random. In other words, to understand H, you actually have to “dig deeper” and study P. H is the visible part of an iceberg, P is the submerged part. You have to weigh together all the programs that give x, not just look at the minimum-size ones, even if you’re only interested in the minimum-size ones!

For any such machine C we also have a “halting probability”:



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