Space Hierarchy Results for Randomized Models

Jeff Kinne & Dieter Van Melkebeek
We prove space hierarchy and separation results for randomized and other semantic models of computation with advice. Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems are the following. Let $s(n)$ be any space-constructible function that is $Omega(log n)$ and such that $s(a n) = O(s(n))$ for all constants $a$, and let $s'(n)$ be any function...