Article
Актуальные приёмы оформления модных шоу в 1991-1995 гг.: предыстория применения информационных технологий
Успехи современной науки и образования. 2016. Т. 5. № 11. С. 163-167.
Макаров С. Л., Макарова Т. Л.
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Bauwens B., Makhlin A., Vereshchagin N. et al. Electronic Colloquium on Computational Complexity. Technical report. Hasso-Plattner-Institut, 2013. No. TR13-007.
Given a machine $U$, a $c$-short program for $x$ is a string $p$ such that $U(p)=x$ and the length of $p$ is bounded by $c$ + (the length of a shortest program for $x$). We show that for any universal machine, it is possible to compute in polynomial time on input $x$ a list of polynomial size guaranteed to contain a $O(\log |x|)$-short program for $x$. We also show that there exist computable functions that map every $x$ to a list of size $O(|x|^2)$ containing a $O(1)$-short program for $x$ and this is essentially optimal because we prove that such a list must have size $\Omega(|x|^2)$. Finally we show that for some machines, computable lists containing a shortest program must have length $\Omega(2^{|x|})$.
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