 If random bits are in short supply, the Chen-Kao algorithm (over the rationals) or the Lewin-Vadhan algorithm (over any field) require fewer random bits at the cost of more required runtime.A "sparse PIT" has at most formula_16 nonzero monomial terms.A sparse PIT can be deterministically solved in polynomial time of the size of the circuit and the number formula_16 of monomials, see also.