  It has been shown that uniform as well as non-uniform cellular automata (CA)
can be evolved to perform certain computational tasks. Random Boolean networks
are a generalization of two-state cellular automata, where the interconnection
topology and the cell's rules are specified at random. Here we present a novel
analytical approach to find the local rules of random Boolean networks (RBNs)
to solve the global density classification and the synchronization task from
any initial configuration. We quantitatively and qualitatively compare our
results with previously published work on cellular automata and show that
randomly interconnected automata are computationally more efficient in solving
these two global tasks. Our approach also provides convergence and quality
estimates and allows the networks to be randomly rewired during operation,
without affecting the global performance. Finally, we show that RBNs outperform
small-world topologies on the density classification task and that they perform
equally well on the synchronization task. Our novel approach and the results
may have applications in designing robust complex networks and locally
interacting distributed computing systems for solving global tasks.
