Downward Collapse from a Weaker Hypothesis
| dc.creator | Hemaspaandra, Edith | |
| dc.creator | Hemaspaandra, Lane A. | |
| dc.creator | Hempel, Harald | |
| dc.date | 1998-08-24 | |
| dc.date.accessioned | 2026-07-07T03:23:28Z | |
| dc.date.available | 2026-07-07T03:23:28Z | |
| dc.description | Hemaspaandra et al. proved that, for $m > 0$ and $0 < i < k - 1$: if $Σ_i^p \BoldfaceDelta DIFF_m(Σ_k^p)$ is closed under complementation, then $DIFF_m(Σ_k^p) = coDIFF_m(Σ_k^p)$. This sharply asymmetric result fails to apply to the case in which the hypothesis is weakened by allowing the $Σ_i^p$ to be replaced by any class in its difference hierarchy. We so extend the result by proving that, for $s,m > 0$ and $0 < i < k - 1$: if $DIFF_s(Σ_i^p) \BoldfaceDelta DIFF_m(Σ_k^p)$ is closed under complementation, then $DIFF_m(Σ_k^p) = coDIFF_m(Σ_k^p)$. | |
| dc.identifier | https://arxiv.org/abs/cs/9808002 | |
| dc.identifier | http://arxiv.org/abs/cs/9808002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/32952 | |
| dc.subject | Computational Complexity | |
| dc.subject | F.1.3 | |
| dc.title | Downward Collapse from a Weaker Hypothesis | |
| dc.type | text |