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Title: Finitely Presented Algebras and the Polynomial Time Hiercharchy
Authors: Kozen, Dexter
Keywords: computer science
technical report
Issue Date: Mar-1977
Publisher: Cornell University
Abstract: Let $S_{n}(V_{n})=\{less than \Gamma, Q_{1}v_{1}\cdots Q_{k}v_{k} s \equiv j greater than | \Gamma$ 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].
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