Kozen, Dexter2007-04-232007-04-231977-03http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR77-303https://hdl.handle.net/1813/7030Let $S_{n}(V_{n})=\{less than \Gamma, Q_{1}v_{1}\cdots Q_{k}v_{k} s \equiv j greater than | \Gamma$ is a finite presentation of $\cal A, Q_{1} \cdots Q_{k}$ is a string of quantifiers with $n$ alterations, the outermost an $\exists (\forall), \cal A \Gamma Q_{1} v_{1} \cdots Q_{k} v_{k} s \equiv t\}$. It is shown that $S_{n} (V_{n})$ is complete for $\Sigma^{P}_{n} (\Pi^{P}_{n})$, and $\stackrel{\stackrel{\infty}{\bigcup}}{n=0} S_{n} \cup V_{n}$ is complete for PSPACE, answering a question of [1] and generalizing a result of Stockmeyer and Meyer [2].951507 bytes411537 bytesapplication/pdfapplication/postscripten-UScomputer sciencetechnical reporttechnical report