Inapproximability Results for Equations over Finite Groups
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by Lars Engebretsen A, Jonas Holmerin A Alex, Er Russell B
http://www.nada.kth.se/~enge/papers/NonAbelian.pdf
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Abstract:
An equation over a finite group G is an expression of form w1w2... wk = 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 | − ɛ for any ɛ> 0. This generalizes results of Håstad (2001, J. ACM, 48 (4)), who established similar bounds under the added condition that the group G is Abelian.
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