Downward Collapse from a Weaker Hypothesis

dc.creatorHemaspaandra, Edith
dc.creatorHemaspaandra, Lane A.
dc.creatorHempel, Harald
dc.date1998-08-24
dc.date.accessioned2026-07-07T03:23:28Z
dc.date.available2026-07-07T03:23:28Z
dc.descriptionHemaspaandra 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.identifierhttps://arxiv.org/abs/cs/9808002
dc.identifierhttp://arxiv.org/abs/cs/9808002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/32952
dc.subjectComputational Complexity
dc.subjectF.1.3
dc.titleDownward Collapse from a Weaker Hypothesis
dc.typetext

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