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Strong self-reducibility precludes strong immunity

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Abstract

Do self-reducible sets inherently lack immunity from deterministic polynomial time? Though this is unlikely to be true in general, in this paper we prove that sufficiently strong self-reducibility precludes sufficiently strong immunity from deterministic polynomial time. In particular, we prove that NT isnot P balanced immune. However, we prove that NT, a class whose sets have very strong self-reducibility properties, is P bi-immune relative to a generic oracle. Thus, the previous result cannot be relativizably extended to bi-immunity. We also prove that NP and ⊕P are both P balanced immune relative to a random oracle; the former provides the strongest known relativized separation of NP from P.

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Authors and Affiliations

  1. Department of Computer Science, University of Rochester, 14627, Rochester, NY, USA

    L. A. Hemaspaandra & M. Zimand

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  1. L. A. Hemaspaandra
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  2. M. Zimand
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Additional information

Supported in part by Grants NSF-CCR-8957604, NSF-INT-9116781/JSPS-ENG-207, NSF-INT-9513368/DAAD-315-PRO-fo-ab, and NSF-CCR-9322513.

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Hemaspaandra, L.A., Zimand, M. Strong self-reducibility precludes strong immunity. Math. Systems Theory 29, 535–548 (1996). https://doi.org/10.1007/BF01184814

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