My question about well-known theorems:
Theorem: Kolmogorov complexity is not a computable function.
And, related, Chaitin's incompleteness theorem.
In both cases constructed programs and proofs based on paradoxical inequality
I'm embarrassed by following thoughts:
For manipulation(processing) of strings, these programs must "know" the size of strings(type of string) that they generate. Or places in memory(linear memory) where string starts and ends. This is impotrant for KolmogorovComplexity subroutine.
But a priori program do "not know" size of string that will satisfy the condition:
Thus, program must to reserve the memory for infinity inductive type, used as:
$...for \ i=1\ to\ infinity:...$
and we obtain:
$log(∞)$ means "size" of unbounded strings' buffer
Thus, program GenerateParadoxicalString has infinite size and never stop.
Infinite size due to GenerateComplexString, because of unbounded buffer.
And never stop due to KolmogorovComplexity, in attempt to read string from unbounded buffer.
Is it correct?