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P versus PSPACE

Let $P$ be deterministic polynomial time and $PSPACE$ deterministic polynomial space.

Is $P = PSPACE$ ?

Abstract

PSPACE permits polynomial memory and potentially exponential time. Quantified Boolean Formula is PSPACE-complete, providing a concrete representative for the question.

Background and progress

Polynomial-space computation emerged as a central resource-bounded model.
Quantified Boolean Formula was shown PSPACE-complete.
The time and space hierarchy theorems separate some resource bounds, but do not separate P from PSPACE.

Reference papers

Complexity Zoo: PSPACEScott AaronsonComplexity Zoo · 2002 ↗

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