  We consider labelings of a finite regular tree by a finite alphabet subject
to restrictions specified by a nonnegative transition matrix, propose an
algorithm for determining whether the set of possible configurations on the
last row of the tree is independent of the symbol at the root, and prove that
the algorithm succeeds in a bounded number of steps, provided that the
dimension of the tree is greater than or equal to the maximum row sum of the
transition matrix. (The question was motivated by calculation of topological
pressure on trees and is an extension of the idea of primitivity for
nonnegative matrices.)
