Abstract
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.
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Engebretsen, L., Holmerin, J., Russell, A. (2002). Inapproximability Results for Equations over Finite Groups. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_8
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DOI: https://doi.org/10.1007/3-540-45465-9_8
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