  Network of neurons in the brain apply - unlike processors in our current
generation of computer hardware - an event-based processing strategy, where
short pulses (spikes) are emitted sparsely by neurons to signal the occurrence
of an event at a particular point in time. Such spike-based computations
promise to be substantially more power-efficient than traditional clocked
processing schemes. However it turned out to be surprisingly difficult to
design networks of spiking neurons that are able to carry out demanding
computations. We present here a new theoretical framework for organizing
computations of networks of spiking neurons. In particular, we show that a
suitable design enables them to solve hard constraint satisfaction problems
from the domains of planning - optimization and verification - logical
inference. The underlying design principles employ noise as a computational
resource. Nevertheless the timing of spikes (rather than just spike rates)
plays an essential role in the resulting computations. Furthermore, one can
demonstrate for the Traveling Salesman Problem a surprising computational
advantage of networks of spiking neurons compared with traditional artificial
neural networks and Gibbs sampling. The identification of such advantage has
been a well-known open problem.
