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Downward Collapse from a Weaker Hypothesis | | Edith Hemaspaandra
; Lane A. Hemaspaandra
; Harald Hempel
; | | Date: |
24 Aug 1998 | | Subject: | Computational Complexity ACM-class: F.1.3 | cs.CC | | Abstract: | Hemaspaandra et al. proved that, for $m > 0$ and $0 < i < k - 1$: if $Sigma_i^p BoldfaceDelta DIFF_m(Sigma_k^p)$ is closed under complementation, then $DIFF_m(Sigma_k^p) = coDIFF_m(Sigma_k^p)$. This sharply asymmetric result fails to apply to the case in which the hypothesis is weakened by allowing the $Sigma_i^p$ 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 $DIFF_s(Sigma_i^p) BoldfaceDelta DIFF_m(Sigma_k^p)$ is closed under complementation, then $DIFF_m(Sigma_k^p) = coDIFF_m(Sigma_k^p)$. | | Source: | arXiv, cs.CC/9808002 | | Services: | Forum | Review | PDF | Favorites | |
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