A Critique of Sopin's "$\mathrm{PH}=\mathrm{PSPACE}$"

Abstract

We critique Valerii Sopin's paper "$\mathrm{PH}=\mathrm{PSPACE}$" [Sop14]. The paper claims to resolve one of the major open problems of theoretical computer science by leveraging the Skolemization of existential quantifiers of quantified boolean formulas to show that $\mathrm{QBF}$ (a well-known $\mathrm{PSPACE}$-complete problem) is in ${\Pi }_4^p$, and thus $\mathrm{PH}=\mathrm{PSPACE}$. In this critique, we highlight problems in that paper and conclude that it fails to establish that $\mathrm{PH}=\mathrm{PSPACE}$.