Inapproximability Results for Equations over Finite Groups

  • Lars Engebretsen
  • Jonas Holmerin
  • Alexander Russell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2380)


An equation over a finite group G is an expression of form w 1 w 2...w k = 1g, where each w i is a variable, an inverted variable, or a constant from G; such an equation is satisfiable if there is a setting of the variables to values in G so that the equality is realized. We study the problem of simultaneously satisfying a family of equations over a finite group G and show that it is NP-hard to approximate the number of simultaneously satisfiable equations to within |G| − ∈ for any ∈ > 0. This generalizes results of Håstad, who established similar bounds under the added condition that the group G is Abelian.


Irreducible Representation Finite Group Constraint Satisfaction Problem Proof System Acceptance Probability 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Lars Engebretsen
    • 1
  • Jonas Holmerin
    • 1
  • Alexander Russell
    • 2
  1. 1.Department of Numerical Analysis and Computer ScienceRoyal Institute of TechnologyStockholmSweden
  2. 2.Department of Computer Science and EngineeringUniversity of ConnecticutStorrs

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