Inapproximability Results for Equations over Finite Groups

Authors:
Lars Engebretsen;Jonas Holmerin;Alexander Russell
Affiliations:
-;-;-
Venue:
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Year:
2002

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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|-驴 for any 驴 0. This generalizes results of H氓stad, who established similar bounds under the added condition that the group G is Abelian.