range problem

A range problem is a weakened form of a search problem. It consists of two functions fl and fu (the lower and upper bounds) and a linear orderingPlanetmathPlanetmath < on the ranges of f1 and f2. A Turing machineMathworldPlanetmath solves a range problem if, for any x, the machine eventually halts with an output y such that f1(x)<y<f2(x).

For example, given any function f with range in and any g:, the strong range problem StrongRangeg(f) is given by lower bound f(x)(1-11-g(|x|)) and upper bound f(x)(1-11+g(|x|)) (note that g is passed the length of x, not the value, which need not even be a number).

Title range problem
Canonical name RangeProblem
Date of creation 2013-03-22 13:02:25
Last modified on 2013-03-22 13:02:25
Owner Henry (455)
Last modified by Henry (455)
Numerical id 5
Author Henry (455)
Entry type Definition
Classification msc 68Q25
Defines strong range problem
Defines strong range