A Statistical Mechanical Interpretation of Algorithmic Information Theory by Kohtaro Tadaki

Author:Kohtaro Tadaki
Language: eng
Format: epub, pdf
ISBN: 9789811507397
Publisher: Springer Singapore

for every and every with . Therefore, the condition (iii) of Theorem 5.11 and the condition (iii) of Theorem 5.14 hold for g.

Thus, Theorem 5.11, Theorem 5.13, and Theorem 5.14 result in Theorem 5.3, Theorem 5.4, and Theorem 5.5, respectively. Then, as we saw in Sect. 5.1, Theorem 5.1 follows immediately from the latter three theorems.

5.4 Some Properties of the Sufficient Conditions

In this section, we investigate some properties of the sufficient conditions for T to be a fixed point in the fixed point theorems on partial randomness; Theorems 5.1, 5.7, 5.8, and 5.9. We can show Theorems 5.24, 5.25, and 5.26 below for the sufficient conditions, in addition to Theorem 5.2 shown already for the sufficient condition regarding the partition function Z(T) of AIT in Sect. 5.1.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.