  Realization of universal computing units for nanorobots is highly promising
in creating new and wide arrays of applications, particularly in the realm of
distributed computation. However, such realization is also a challenging
problem due to the physical limitations of nanometer-sized designs such as in
computation, sensory and perception as well as actuation. This paper proposes a
theoretical foundation for solving this problem based on a novel notion of
distributed swarm computing by basis agents (BAs). The proposed BA is an
abstract model for nanorobots that can compute a very simple basis function
called B-function. It is mathematically shown here that a swarm of BAs has the
universal function approximation property and can accurately approximate
functions. It is then analytically demonstrated that a swarm of BAs can be
easily reprogrammed to compute desired functions simply by adjusting the
concentrations of BAs in the environment. We further propose a specific
structure for BAs which enable them to perform distributed computing such as in
the aqueous environment of living tissues and nanomedicine. The hardware
complexity of this structure aims to remain low to be more reasonably
realizable by today technology. Finally, the performance of the proposed
approach is illustrated by a simulation example.
