  In present day technology, storing and processing of information occur on
physically distinct regions of space. Not only does this result in space
limitations; it also translates into unwanted delays in retrieving and
processing of relevant information. There is, however, a class of two-terminal
passive circuit elements with memory, memristive, memcapacitive and
meminductive systems -- collectively called memelements -- that perform both
information processing and storing of the initial, intermediate and final
computational data on the same physical platform. Importantly, the states of
these memelements adjust to input signals and provide analog capabilities
unavailable in standard circuit elements, resulting in adaptive circuitry, and
providing analog massively-parallel computation. All these features are
tantalizingly similar to those encountered in the biological realm, thus
offering new opportunities for biologically-inspired computation. Of particular
importance is the fact that these memelements emerge naturally in nanoscale
systems, and are therefore a consequence and a natural by-product of the
continued miniaturization of electronic devices. We will discuss the various
possibilities offered by memcomputing, discuss the criteria that need to be
satisfied to realize this paradigm, and provide an example showing the solution
of the shortest-path problem and demonstrate the healing property of the
solution path.
