Circumventing d-to-1 for Approximation Resistance of Satisfiable Predicates Strictly Containing Parity of Width Four

(Extended Abstract)
  • Cenny Wenner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7408)

Abstract

Håstad established that any predicate P ⊆ {0,1}m containing parity of width at least three is approximation resistant for almost satisfiable instances. However, in comparison to for example the approximation hardness of Max-3SAT, the result only holds for almost satisfiable instances. This limitation was mitigated by O’Donnell, Wu, and Huang under the d-to-1 Conjecture. They showed the threshold result that if a predicate \(\textit{strictly}\) contains parity of width at least three, then it is approximation resistant also for satisfiable instances. We extend modern hardness of approximation techniques by Mossel et al. to projection games, eliminating dependencies on the degree of projections via Smooth Label Cover, and prove unconditionally the same approximation resistance result for predicates of width four.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Cenny Wenner
    • 1
    • 2
  1. 1.KTH – Royal Institute of TechnologySweden
  2. 2.Stockholm UniversitySweden

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