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Results tagged with kolmogorov-complexity
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user 79425
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.
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Kolmogorov complexity of prefixes of computable sequences
Let the characteristic sequence of a set $A ⊆ \mathbb{Z^+}$ be the following infinite binary sequence:
$$χ_A = b_1b_2b_3\ldots,$$
whose $n$th bit is 1 if $n ∈ A$ And 0 otherwise.
Write $χ_{A,n}$ for …
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Non Regularity proof using Kolmogorov Complexity (Li - Vitanyi Theorem)
When proving a language is non regular we can use Kolmogorov complexity.
As far I know to do this we just have to use this satisfy the following conditions
Given $Y^A_{x,n}$= the nth string $y∈Σ^∗$ (i …
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Prove that A is non-regular using K-Complexity Non regularity theorem
Given $Y^A_{x,n}$= the nth string $y∈Σ^∗$ (in lex order) such that $xy∈A$ (if n such y exits). So what completes $x$ if adding $n$ such $y$'s brings us to an element in the set $A$
Given $A \subseteq …
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Kolmogorov Complexity proving there exists a constant for when if two strings are equal length
When talking about kolmogorov complexity, I understand that it describes true randomness of given (for now) a string $x$, if we can describe x in less than the $|x|$ then its complexity is said to be
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