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Helping by unambiguous computation and probabilistic computation

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Abstract

Schöning [S] introduced a notion of helping and suggested the study of the class Phelp(C) of languages that can be helped by oracles in a given classC. He showed that Phelp(BPP) is included in ZPP. Later, Ko [K] introduced a weaker notion of helping, called one-sided helping, and proved that P1-help(BPP) is included in R and that UP is included in P1-help(UP). The three inverse inclusions are open problems (see [Hem]). Caiet al. [CHV] constructed a relativized world in which the third open inclusion fails. We show relativized worlds in which all three open inclusions fail in a strong way. In particular, we strengthen the result of Caiet al., showing that Phelp(UP) is not included in Few. This is obtained as a corollary of a general result that gives sufficient conditions, on a relativizable complexity classC, to ensure the relativized separation of Phelp(UP) fromC. Further separations are also derived. The other two open inclusions are showed to fail strongly by the relativized separation of ZPP from P1-help(AM ∩ co-AM).

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università di Camerino, Via Madonna delle Carceri, 62032, Camerino (MC), Italy

    P. Cintioli

  2. Dipartimento di Scienze dell’Informazione, Università di Roma “La Sapienza”, Via Salaria 113, I-00198, Roma, Italy

    R. Silvestri

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  1. P. Cintioli
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  2. R. Silvestri
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Cintioli, P., Silvestri, R. Helping by unambiguous computation and probabilistic computation. Theory of Computing Systems 30, 165–180 (1997). https://doi.org/10.1007/BF02679447

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