Wikipedia:Reference desk/Archives/Mathematics/2012 August 8#Stupid Universal Turing Machine

For every string $x$, show that there exists a universal Turing machine $U$ such that $K\_U(x)\; :=\; \backslash min\_p\backslash \{l(p):U(p)=x\backslash \}\; =\; 1$. --150.203.114.14 (talk) 06:39, 8 August 2012 (UTC)

:For any turing machine A, B and recursive set R there is a machine C so C(p) = A(p) if p is in R and B(p) otherwise. Thus, let R be the set {1}, A so A(p) = x for all x and B the composition UD, U a universal machine and D sending p > 1 to p-1 and 1 to whatever. Or, given U, in words: if p = 1 output x; if p > 1, output U(p - 1). Phoenixia1177 (talk) 08:52, 8 August 2012 (UTC)

How exactly do I test for this? Our article doesn't seem to elucidate this. Also, the MATLAB function ranksum() only gives a two-sided p-value (testing H0 that the distributions are the same). However I would like to examine whether one distribution tends to be greater than the other. I would like to know the appropriate formulas, and also how I would calculate this in a MATLAB script. Nothing gold can stay (talk) 18:13, 8 August 2012 (UTC)

Can it be done without assuming a normal distribution? Nothing gold can stay (talk) 18:31, 8 August 2012 (UTC)