A space optimal algorithm to solve a problem
Abstract
Given a semi-decidable relation $R$, and a string $x$, deciding wether or not there is a witness $y$ such that $(x,y) \in R$ is a very hard problem. However, Leonid Levin has constructed a time optimal algorithm to solve the above question. The algorithms is not based on a brute-force search but on testing programs that generate witness. Following Levin's work, we define a space-efficient algorithm that solves the above question. Then, we discuss on the ability to improve Savitch's Theorem