If NL = P, how do we prove that P != PSPACE? Do we have to use Savitch's theorem?
2026-03-30 06:09:19.1774850959
If NL = P, prove that P!=PSPACE
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By Savitch's theorem, $NL \subseteq DSPACE(\log^2 n)$, and, by a diagonalization argument, $DSPACE(\log^2 n) \subsetneq PSPACE$. So, $NL\subsetneq PSPACE$, and, if $NL=P$, $P\subsetneq PSPACE$.