  We present some combinatorial results on the stochastic abelian sandpile
model. These models are characterized by nondeterministic toppling rules. The
recurrence checking for the deterministic case can be performed using the well
known burning test which detects presence of forbidden sub-configurations (FSC)
in strongly polynomial time. In the stochastic case, however, even for Manna's
model, which is perhaps the simplest non-trivial example, no such procedure is
known. In this paper, we address the decision problem of the existence of any
FSC in a general stochastic sandpile. We demonstrate a polynomial time
algorithm which, given the sandpile graph and toppling rules, decides if there
exists an FSC. In the event of a positive answer, it generates at least one FSC
for the given sandpile. Repeated application of the algorithm can be used to
find many distinct FSCs. We also demonstrate a procedure for creating larger
FSCs from smaller ones and use this to create FSCs for the Manna's model. We
hope that the structural analysis of stochastic sandpile we perform in this
paper, will prove useful in the eventual formulation of a deterministic
procedure to decide recurrence.
