  We present a computational method for finding attractors (ergodic sets of
states) of Boolean networks under asynchronous update. The approach is based on
a systematic removal of state transitions to render the state transition graph
acyclic. In this reduced state transition graph, all attractors are fixed
points that can be enumerated with little effort in most instances. This
attractor set is then extended to the attractor set of the original dynamics.
Our numerical tests on standard Kauffman networks indicate that the method is
efficient in the sense that the total number of state vectors visited grows
moderately with the number of states contained in attractors.
