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1989•SIAM Journal on ComputingRequires access

Relativized Polynomial Time Hierarchies Having Exactly K Levels

Ker‐I Ko

Open publisher page 57 citations

Abstract

It is proved that for every integer $k \geqq 0$, there is an oracle $A_k $ relative to which the polynomial time hierarchy collapses so that it has exactly k levels. Furthermore, sets $B_k $ and $C_k $ may be constructed so that, relative to $B_k $, the polynomial time hierarchy has exactly k levels and the class PSPACE coincides with the polynomial time hierarchy, and, relative to $C_k $, the polynomial time hierarchy has exactly k levels and the class PSPACE is different from the polynomial time hierarchy.

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What this paper is about

It is proved that for every integer $k \geqq 0$, there is an oracle $A_k $ relative to which the polynomial time hierarchy collapses so that it has exactly k levels. Furthermore, sets $B_k $ and $C_k $ may be constructed so that, relative to $B_k $, the polynomial time hierarchy has exactly k levels and the class PSPACE coincides with the polynomial time hierarchy, and, relative to $C_k $, the polynomial time hierarchy has exactly k levels and the class PSPACE is different from the polynomial time hierarchy.

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OpenAlex reports 57 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

It is proved that for every integer $k \geqq 0$, there is an oracle $A_k $ relative to which the polynomial time hierarchy collapses so that it has exactly k levels. Furthermore, sets $B_k $ and $C_k $ may be constructed so that, relative to $B_k $, the polynomial time hierarchy has exactly k levels and the class PSPACE coincides with the polynomial time hierarchy, and, relative to $C_k $, the polynomial time hierarchy has exactly k levels and the class PSPACE is different from the polynomial time hierarchy.

Key concepts: Hierarchy, PSPACE, Mathematics, Combinatorics, Time complexity, Polynomial hierarchy, Complexity class, Polynomial

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