section provides a short description of Random Boolean Networks,
their properties and some terminology.
Boolean Networks - a short outline
Random Boolean Networks
(RBN) are also known as NK-Networks and were first proposed by S.A
[B2]) in 1969 to model genetic regulation in cells. RBN are often specified by two parameters: N,
the number of nodes and K, the number of incoming links per node.
Sometimes, K also indicates the average number of incoming
connections per node. Each node has a specific logic transition
rule that determines the output and the state of the node in
function of the values on the incoming links. The values taken by
the outputs and, therefore also by the connections, are zero and
Connections and rules in a RBN are chosen at random. For a node
with K incoming links there are 2^K possible sets of input vectors
and the number of values in the rules of the network is N*2^K.
Considering that each of these values can be zero ore one, there
are 2^(N*2^K) different networks that can be created at random.
RBN can be regarded as binary neural networks
and are therefore forming a subclass of neural networks. Comparing
to neural nets, RBN do not have weighted connections and are
consequently not suited for learning tasks. However, RBN can be
used to study large systems of many interacting units and their
dynamics (e.g gene regulation networks, neural networks,
economics, etc.). Kauffman's studies ([B1])
have revealed surpisingly
ordered structures in randomly constructed networks. It turned out
that the networks exhibit three major regimes of behaviour: ordered
(solid), complex (liquid) and chaotic (gas). The
most highly organized behaviour appears to occur in networks where
each node receives inputs from two other nodes (K=2).
RBN cannot only be seen as subclass of neural
networks, but also as a generalization of the well-known Cellular
Automata (CA) proposed by John von Neumann in the late 1940's. In this case a node only receives inputs from nodes
in his local (spatial) neighbourhood and each node has the same
logic transition rule.
Different types of RBN can be classified according
to their update schemes.