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Hardness of approximating Σ2p minimization problems

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1 Author(s)
Umans, C. ; Comput. Sci. Div., California Univ., Berkeley, CA, USA

We show that a number of natural optimization problems in the second level of the Polynomial Hierarchy are Σ2p -hard to approximate to within nε factors, for specific ε>0. The main technical tool is the use of explicit dispersers to achieve strong, direct inapproximability results. The problems we consider include Succinct Set Cover, Minimum Equivalent DNF, and other problems relating to DNF minimization. Under a slightly stronger complexity assumption, our method gives optimal n1-ε inapproximability results for some of these problems. We also prove inapproximability of a variant of an NP optimization problem, Monotone Minimum Satisfying Assignment, to within an nε factor using the same technique

Published in:

Foundations of Computer Science, 1999. 40th Annual Symposium on

Date of Conference:

1999