Editing Savitch's theorem (section)

== Corollaries ==
Some important corollaries of the theorem include:
; [[PSPACE]] = [[NPSPACE]]
: That is, the languages that can be recognized by deterministic polynomial-space Turing machines and nondeterministic polynomial-space Turing machines are the same. This follows directly from the fact that the square of a polynomial function is still a polynomial function.{{sfnp|Papadimitriou|1993}} It is believed that a similar relationship  does not exist between the polynomial time complexity classes, [[P (complexity)|P]] and [[NP (complexity)|NP]], although this is still an [[P = NP problem|open question]].
; [[NL (complexity)|NL]] ⊆ [[L (complexity)|L<sup>2</sup>]]
: That is, all languages that can be solved nondeterministically in logarithmic space can be solved deterministically in the complexity class <math display=block>\mathsf{\color{Blue}L}^2 =\mathsf{DSPACE}\left(\left(\log n\right)^2\right).</math> This follows from the fact that STCON is [[NL-complete]].