10.4230/LIPIcs.STACS.2008.1363
Kinne, Jeff
van Melkebeek, Dieter
Space Hierarchy Results for Randomized Models
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany
2008
Computer Science
000 Computer science, knowledge, general works
Herbstritt, Marc
2008-02-06
eng
ConferencePaper
12 pages
application/pdf
1.0
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC-BY-NC-ND)
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 that is $omega(s(n))$.
- There exists a language computable by two-sided error randomized
machines using $s'(n)$ space and one bit of advice that is not
computable by two-sided error randomized machines using $s(n)$
space and $min(s(n),n)$ bits of advice.
- There exists a language computable by zero-sided error randomized
machines in space $s'(n)$ with one bit of advice that is not
computable by one-sided error randomized machines using $s(n)$
space and $min(s(n),n)$ bits of advice.
The condition that $s(a n)=O(s(n))$ is a technical condition
satisfied by typical space bounds that are at most linear. We also
obtain weaker results that apply to generic semantic models of
computation.