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
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.
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.