Finitely Presented Algebras and the Polynomial Time Hiercharchy

• Authors: Dexter Kozen
• Venue: Finitely Presented Algebras and the Polynomial Time Hiercharchy
• Year: 1977

Let $S_{n}(V_{n})=\{ | \Gamma$ 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].