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Results tagged with kolmogorov-complexity
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user 56328
11
votes
3
answers
709
views
natural metrics for proof length
I am trying to make my way into Homotopy Type Theory(HoTT) where a mathematician may view proofs as paths. Intuitively, this leads me to the idea of a metric on the space of mathematical propositions. …
- 3,871
1
vote
Accepted
natural metrics for proof length
Inspired by the informal notion of Cognitive distance, in 2010 Charles Bennett, Peter Gács, Ming Li, Paul Vitanyí and Wojcech Zurech introduced the notion of Information Distance which was used in the …
- 3,871
6
votes
2
answers
794
views
Kolmogorov's approach to probability theory
Question:
Did Kolmogorov develop a set of axioms for probability theory motivated by Algorithmic Information Theory in the 1960s?
Context:
In 1965, Andrey Kolmogorov considered three approaches to inf …
- 3,871
6
votes
Accepted
Kolmogorov's approach to probability theory
In 1970, Kolmogorov developed the 'Combinatorial foundations of information theory and the calculus of probabilities' in relation to a presentation at the International Congress of Mathematicians in N …
- 3,871
4
votes
1
answer
677
views
Proof that dynamical systems with bounded Kolmogorov complexity can't emulate all Turing mac...
Motivation:
During a discussion with neuroscientists the question arose as to whether the human brain may emulate any Turing machine. If we assume that animal brains may be modelled as deterministic …
- 3,871
5
votes
0
answers
301
views
The expressiveness of functions computable on trees
Motivation:
Let's define a function computable on a $k$-ary tree as a function composed with simpler computable functions defined at each node such that a function of this kind defined on a binary tre …
- 3,871