  In the applications of Boolean networks to modeling biological systems, an
important computational problem is the detection of the fixed points of these
networks. This is an NP-complete problem in general. There have been various
attempts to develop algorithms to address the computation need for large size
Boolean networks. The existing methods are usually based on known algorithms
and thus limited to the situations where these known algorithms can apply. In
this paper, we propose a novel approach to this problem. We show that any
system of Boolean equations is equivalent to one Boolean equation, and thus it
is possible to divide the polynomial equation system which defines the fixed
points of a Boolean network into subsystems that can be solved easily. After
solving these subsystems and thus reducing the number of states, we can combine
the solutions to obtain all fixed points of the given network. This approach
does not depend on other algorithms and it is straightforward and easy to
implement. We show that our method can handle large size Boolean networks, and
demonstrate its effectiveness by using MAPLE to compute the fixed points of
Boolean networks with hundreds of nodes and thousands of interactions.
