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

Abstract

We critique Valerii Sopin's paper "${\rm PH} = {\rm PSPACE}$" [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 ${\rm QBF}$ (a well-known ${\rm PSPACE}$-complete problem) is in $\Pi_4^p$, and thus ${\rm PH} = {\rm PSPACE}$. In this critique, we highlight problems in that paper and conclude that it fails to establish that ${\rm PH} = {\rm PSPACE}$.