  A great deal remains open about computational complexity. We know that strictly more of a particular computational resource lets us solve strictly harder problems, e.g. \(\TIME[n]\) is strictly contained in \(\TIME[n^{1.01}]\) and similarly for \(\SPACE\) and other measures. However, the trade-offs between different computational resources is still quite poorly understood. It is obvious that \(\P\) is contained in \(\NP\). Furthermore, \(\NP\) is contained in \(\PSPACE\) because in \(\PSPACE\) we can systematically try every single branch of an \(\NP\) computation, reusing space for the successive branches, and accepting if any of these branches lead to acceptance. \(\PSPACE\) is contained in \(\EXPTIME\) because if a \(\PSPACE\) machine takes more than exponential time, then it has exactly repeated some configuration so it must be in an infinite loop. The following are the known relationships between the above classes: