TY - GEN

T1 - Downward separation fails catastrophically for limited nondeterminism classes

AU - Beigel, R.

AU - Goldsmith, J.

PY - 1994

Y1 - 1994

N2 - The β hierarchy consists of sets βk = NP[logk n] NP. Unlike collapses in the polynomial hierarchy and the Boolean hierarchy, collapses in the β hierarchy do not seem to translate up, nor does closure under complement seem to cause the hierarchy to collapse. For any consistent set of collapses and separations of levels of the hierarchy that respects P = β1 β2 ··· NP, we can construct an oracle relative to which those collapses and separations hold, yet any (or all) of the βk's are closed under complement. To give a few relatively tame examples: For any k≥1, we construct an oracle relative to which.

AB - The β hierarchy consists of sets βk = NP[logk n] NP. Unlike collapses in the polynomial hierarchy and the Boolean hierarchy, collapses in the β hierarchy do not seem to translate up, nor does closure under complement seem to cause the hierarchy to collapse. For any consistent set of collapses and separations of levels of the hierarchy that respects P = β1 β2 ··· NP, we can construct an oracle relative to which those collapses and separations hold, yet any (or all) of the βk's are closed under complement. To give a few relatively tame examples: For any k≥1, we construct an oracle relative to which.

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M3 - Conference contribution

AN - SCOPUS:0028590463

SN - 0818656727

T3 - Proceedings of the IEEE Annual Structure in Complexity Theory Conference

SP - 134

EP - 138

BT - Proceedings of the IEEE Annual Structure in Complexity Theory Conference

A2 - Anon, null

Y2 - 28 June 1994 through 1 July 1994

ER -