On the topology of algorithms, I

We call such an algorithm a computation tree. A computation tree for the problem Poly(d) has input the coefficients of a polynomial f (in terms of real and imaginary parts). The output must consist of (z,, . . . , zd) (again given in terms of real and imaginary parts), each zi being within E of {i, the <i being the roots off. The computation nodes do not contribute to the topology of the computation tree, so we define the topological complexity of the tree, as the number of branching nodes. The topological complexity of problem Poly(d) is the minimum of the topological complexity of all computation trees for that problem.