Query Order in the Polynomial Hierarchy


We study query order within the polynomial hierarchy. P C:D denotes the class of languages computable by a polynomial-time machine that is allowed one query to C followed by one query to D HHW]. We prove that the levels of the polynomial hierarchy are order-oblivious: P p j :: p k = P p k :: p j. Yet, we also show that these ordered query classes form new levels in the polynomial hierarchy unless the polynomial hierarchy collapses. We prove that all leaf language classes|and thus essentially all standard complexity classes|inherit all order-obliviousness results that hold for P.

DOI: 10.1007/BFb0036186

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@inproceedings{Hemaspaandra1997QueryOI, title={Query Order in the Polynomial Hierarchy}, author={Edith Hemaspaandra and Lane A. Hemaspaandra and Harald Hempel}, booktitle={FCT}, year={1997} }