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A second step toward the strong polynomial-time hierarchy

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Abstract

In this paper we discuss the concepts ofimmunity andsimplicity in levels of the relativized Polynomial-time Hierarchy just aboveP. We consider various diagonalization techniques with which oracle sets can be constructed relative to which strong separations between language classes in the first two levels of this hierarchy are established. In particular, we build oracle sets for separation of relativized Σ P2 from relativizedNP with immunity, of relativized Σ P2 from relativizedNP with bi-immunity, of relativized Σ P2 from relativized Δ P2 with immunity, of relativized Π P2 from relativized Δ P2 with immunity, and finally of relativized Σ P2 from relativized Π P2 with simplicity.

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  1. Department of Mathematics and Computer Science, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV, Amsterdam, The Netherlands

    Leen Torenvliet

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  1. Leen Torenvliet
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Torenvliet, L. A second step toward the strong polynomial-time hierarchy. Math. Systems Theory 21, 99–123 (1988). https://doi.org/10.1007/BF02088009

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  • DOI: https://doi.org/10.1007/BF02088009

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