  In this paper we study the strengths and limitations of collaborative teams
of simple agents. In particular, we discuss the efficient use of "ant robots"
for covering a connected region on the $Z^{2}$ grid, whose area is unknown in
advance and which expands stochastically. Specifically, we discuss the problem
where an initial connected region of $S_0$ boundary tiles expand outward with
probability $p$ at every time step. On this grid region a group of $k$ limited
and simple agents operate, in order to clean the unmapped and dynamically
expanding region. A preliminary version of this problem was discussed in
[1],[2] involving a deterministic expansion of a region in the grid.In this
work we extend the model and examine cases where the spread of the region is
done stochastically, where each tile has some probability $p$ to expand, at
every time step. For this extended model we obtain an analytic probabilistic
lower bounds for the minimal number of agents and minimal time required to
enable a collaborative coverage of the expanding region, regardless of the
algorithm used and the robots' hardware and software specifications. In
addition, we present an impossibility result, for a variety of regions that
would be impossible to completely clean, regardless of the algorithm used.
Finally, we validate the analytic bounds using extensive empirical computer
simulation results.
