| | |
Summary: Avoiding Simplicity is Complex
Eric Allender
Department of Computer Science
Rutgers University
Piscataway, NJ 08855, USA
allender@cs.rutgers.edu
Holger Spakowski
Department of Mathematics & Applied Mathematics
University of Cape Town
Rondebosch 7701, South Africa
Holger.Spakowski@uct.ac.za
May 16, 2011
Abstract
It is a trivial observation that every decidable set has strings of length n with
Kolmogorov complexity log n+O(1) if it has any strings of length n at all. Things
become much more interesting when one asks whether a similar property holds
when one considers resource-bounded Kolmogorov complexity. This is the ques-
tion considered here: Can a feasible set A avoid accepting strings of low resource-
bounded Kolmogorov complexity, while still accepting some (or many) strings of
length n?
|
