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computability - Uncomputability of Kolmogorov complexity
2018年9月25日 · That is, we want to show that if we could compute the Kolmogorov complexity of an arbitrary string we could use this to solve the Halting Problem (put another way, we want to reduce the Halting Problem to the Kolmogorov complexity problem). This in fact works, although it takes a bit of thought.
Newest 'kolmogorov-complexity' Questions - Mathematics Stack …
2024年10月4日 · Kolmogorov complexity defines the complexity of things in terms of how many bits it takes to specify them. All integers can be specified using a finite number of bits, proportional to their logarithm. ...
A question on Kolmogorov Complexity - Mathematics Stack …
2014年3月11日 · is a program of length 32 (ignoring the main-part and so on if interpreted as a C-program), and it prints exactly a string of length 32. If this is the shortest possible C-program then its Kolmogorov complexity would be 32. But this is with respect to the C programming language, for another description mechanism this might be different.
information theory - Kolmogorov Complexity and Compression …
2023年1月2日 · To put it in context, the basic reference on Kolmogorov complexity is the book by Li and Vitanyi. Recently, Vitanyi published a review article in the journal Entropy on methods of approximating Kolmogorov complexity. Recently there have been several proposals regarding how to compute or approximate in some fashion the Kolmogorov complexity ...
Kolmogorov complexity of a product of two numbers
It appears that the book is conflating two somewhat different concepts: Kolmogorov complexity and prefix free Kolmogorov complexity. Prefix free Kolmogorov complexity is defined similarly to the usual Kolmgorov complexity, except that you require that the programming language you use has the property that no valid program is a prefix of another ...
reference request - Terminology for the Kolmogorov complexity of ...
2017年6月1日 · Apparently it is possible to use the same set up as in regular definition of Kolmogorov complexity of a finite binary string for the definition of Kolmogorov complexity of a function. The Kolmogorov complexity of an integer valued function f is the length of the shortest program to the turing machine that computes f. For more detail, you can ...
On the Kolmogorov complexity of integers with large prime factors
2023年11月16日 · Well, I found at least one problem. As per Kolmogorov complexity of a product of two numbers, ...
What is the relationship between Kolmogorov Complexity and …
2022年4月23日 · This is the idea behind the absolute Kolmogorov complexity, and the informal construction behind it. But the construction is not complete yet, we have to proof a certain theorem called the invariance theorem.
Kolmogorov complexity of classical music - MathOverflow
2021年10月10日 · So assuming we are comparing recordings of similar duration I would expect in terms of Kolmogorov complexity C(soundtrack of a Billboard Hot 100 song)<C(classical music piece)<C(white noise). Maybe for a meaningful comparison we should also control for the number of instruments used. Has anyone analyzed music from this perspective? P.S.
Relationship between compression, shannon entropy and …
A related thing seems to be Kolmogoroff complexity: The Kolmogorov complexity of a string m is the number of bits which are needed for the shortest program which produces m when executed. How are the two related?