# Questions tagged [kolmogorov-complexity]

The Kolmogorov complexity of a string s is equal to the length of the shortest program computing s and halting. Measures the lack of structure in a string.

12 questions
Filter by
Sorted by
Tagged with
5k views

### What are very short programs with unknown halting status?

This 579-bit program in the Binary Lambda Calculus has unknown halting status: ...
1k views

### Proof of non-regularity, based on the Kolmogorov complexity

In class our professor showed us 3 methods for proving non-regularity: Myhill–Nerode theorem Pumping Lemma for regular languages Proof of non-regularity, based on the Kolmogorov complexity Now the ...
2k views

### Approximating the Kolmogorov complexity

I've studied something about the Kolmogorov Complexity, read some articles and books from Vitanyi and Li and used the concept of Normalized Compression Distance to verify the stilometry of authors (...
365 views

### What's relation between Kolmogorov complexity and pseudorandomness?

In a comment on this question, @Kaveh wondered whether the questioner really wanted to ask "is there a relation between strings with high Kolmogorov complexity and pseudorandomness?" This is not the ...
96 views

### Conditional Kolmogorov compexity of string concatenation

In what follows $K(x|y)$ is conditional Kolmogorov complexity, $xx$ is $x$ concatenated with itself. It appears to me that $K(xx|yy)=K(xx)$ should be true for infinitely many strings $x$ and $y$. In ...
472 views

### What is an estimation of the Kolmogorov Complexity for the first N integers?

I'm aware some ints have higher or lower Kolmogorov Complexities. For example, the number 5.41126806512 has a very low complexity as it can be expressed by ...
423 views

### What problem cannot be solved by a short program?

BACKGROUND: Recently I tried to solve a certain difficult problem that gets as input an array of $n$ numbers. For $n=3$, the only solution I could find was to have a different treatment for each of ...
849 views

### Can a transcendental number like $e$ or $\pi$ be compressed as not algorithmically random?

The related and interesting fields of Information Theory, Turing Computability, Kolmogorov Complexity and Algorithmic Information Theory, give definitions of algorithmically random numbers. An ...
518 views

### What is an example of complex random string, in the Kolmogorov-Chatin sense?

Any string generated from a PRNG clearly has a very short description. You need the code for the random number generator, the seed, and then the number of times to iterate. So, it seems that all ...