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### MINIMUM ATTRACTION RADIUS FOR BINARY HOPFIELD NET

- INSTANCE: An n-node synchronous binary Hopfield network and a stable initial vector of states . A binary Hopfield network is a complete graph where each edge has an integer weight w(vi,vj) and each vertex has an integer threshold value t(vi). At each time step t each vertex vi has a state x(t,vi). x(0,vi) is given by u and where is the sign function. An initial vector of states is stable if x(t,vi) eventually converges for all i.

- SOLUTION: An initial vector of states v that either converges to a different vector than u or is not stable.

- MEASURE: The Hamming distance between u and v. If v is the vector nearest to u that does not converge to the same vector as u, then this distance is the attraction radius.

- Bad News: Not approximable within for any [154].

- Comment: Transformation from MINIMUM INDEPENDENT DOMINATING SET.

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