An equation over a finite group G is an expression of form w 1w2. wκ = 1G, where each wi 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|-ε for any ε > 0. This generalizes results of Håstad, who established similar bounds under the added condition that the group G is Abelian. © 2002 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Engebretsen, L., Holmerin, J., & Russell, A. (2002). Inapproximability results for equations over finite groups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2380 LNCS, pp. 73–84). Springer Verlag. https://doi.org/10.1007/3-540-45465-9_8
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