MS4 M INIMUM A TTRACTION R ADIUS FOR B INARY H OPFIELD N ET

     
• I NSTANCE : 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 and each vertex has an integer threshold value . At each time step t each vertex has a state . is given by u and where is the sign function. An initial vector of states is stable if eventually converges for all i .
• S OLUTION : An initial vector of states v that either converges to a different vector than u or is not stable.
• M EASURE : 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 [ 109 ].
• Comment: Transformation from M INIMUM I NDEPENDENT D OMINATING S ET .