Tagged Questions

92 views

“logical distance” link algorithmic complexity to statistical information [closed]

Someone mentioned what I think was referred to as 'logical distance'. My hard drive crashed and I dont have the link anymore. I do recall that I ran across it on this site, in response to linking ...
586 views

Complexity of convex polytope volume calculation ? (Volume of Voronoi cell) (Error probability)

Assume I have polytope in R^k given by N (k<< N) linear inequalities (A_i x < b_i). I guess complexity of its volume calculate is higher than linear in "N", am I right ? (Is the complexity ...
320 views

compression of a Turing machine run sequence

consider a Turing machine with a set of states $s_n$ and alphabet symbols $a_n$. now consider a "run sequence" generated from a starting input in the following sense. the run sequence is defined as ...
859 views

Distribution of the computable numbers on the real number line

If we order all the positive computable real numbers $r_1,r_2,r_3...$ by their Kolmogorov complexity in some language $L$, then make a histogram plot of the $r_i$ on the real line, and we scale it ...
1k views

Compressing Graphs (Kolmogorov complexity of graphs)

What is known about compressing graphs? Here, with "compressing", I mean something like "putting a graph into a zip program"; or with a more technical expression, what is know about the Kolmogorov ...
810 views

Is pattern recognition NP-complete?

Hello, is the problem of pattern recognition (for a given sequence of n numbers, find the shortest Turing machine with an alphabet of 42 elements that will output these n numbers in, say, 5*n^3 time) ...
I am looking for "low-complexity" indexing methods to enumerate binary sequences of a given length and a given weight. Formally, let $T_k^n = \{x_1^n \in \{0,1\}^n: \sum_{i=1}^n x_i = k\}$. How to ...
Hello, Let T be a Turing machine such that 1) it operates on the alphabet {0,1}, 2) its set of states is A 3) the language it accepts is $L$ . Does there exists a Turing machine S which also ...