# polylogarithmic space [closed]

I apologize if this is a silly question, but could someone tell me whether the class polyL (polylogarithmic space) is equal to the class ATIME(polylog)? If so, where can I find a reference to this or is it obvious?

## closed as off-topic by Raphael, Jan Johannsen, Emil Jeřábek, Kaveh, Yuval FilmusSep 25 '17 at 13:54

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$SPACE[polylog(n)]=ATIME[polylog(n)]$ citing that $ATIME[s(n)]\subseteq SPACE[s(n)]\subseteq ATIME[(s(n))^2]$. This follows from a modified proof of Savitch's Theorem and is a pretty standard exercise in Complexity Theory courses. I'm not sure where this theorem first appeared, but I'll happily add a link to the paper if I find it or if someone links it in the comments.