What's Up with Downward Collapse: Using the Easy-Hard Technique to Link Boolean and Polynomial Hierarchy Collapses

Edith Hemaspaandra; Lane A. Hemaspaandra; Harald Hempel

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What's Up with Downward Collapse: Using the Easy-Hard Technique to Link Boolean and Polynomial Hierarchy Collapses

Edith Hemaspaandra·Lane A. Hemaspaandra·Harald Hempel

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Abstract

During the past decade, nine papers have obtained increasingly strong consequences from the assumption that boolean or bounded-query hierarchies collapse. The final four papers of this nine-paper progression actually achieve downward collapse---that is, they show that high-level collapses induce collapses at (what beforehand were thought to be) lower complexity levels. For example, for each $k\geq 2$ it is now known that if $\psigkone=\psigktwo$ then $\ph=\sigmak$. This article surveys the history, the results, and the technique---the so-called easy-hard method---of these nine papers.

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Edith Hemaspaandra, Lane A. Hemaspaandra, Harald Hempel. 1999-10-01. What's Up with Downward Collapse: Using the Easy-Hard Technique to Link Boolean and Polynomial Hierarchy Collapses. https://arxiv.org/abs/cs/9910002

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