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On the power of parity polynomial time

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Abstract

This paper proves that the complexity class ⊕P, parity polynomial time [PZ], contains the class of languages accepted byNP machines with few accepting paths. Indeed, ⊕P contains a broad class of languages accepted by path-restricted nondeterministic machines. In particular, ⊕P contains the polynomial accepting path versions ofNP, of the counting hierarchy, and of Mod m NP form>1. We further prove that the class of nondeterministic path-restricted languages is closed under bounded truth-table reductions.

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Authors and Affiliations

  1. Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA

    Jin-yi Cai

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

    Lane A. Hemachandra

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  1. Jin-yi Cai
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  2. Lane A. Hemachandra
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Additional information

These results were announced at the 6th Symposium on Theoretical Aspects of Computer Science [CH3]. Jin-yi Cai was supported in part by NSF Grant CCR-8709818 and the work was done while he was at Yale University. Lane A. Hemachandra was supported in part by a Hewlett-Packard Corporation equipment grant and the National Science Foundation under Grant CCR-8809174/CCR-8996198 and a Presidential Young Investigator Award. His work was done in part while at Columbia University.

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Cai, Jy., Hemachandra, L.A. On the power of parity polynomial time. Math. Systems Theory 23, 95–106 (1990). https://doi.org/10.1007/BF02090768

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