A Polynomial Time Deterministic Algorithm for Identity Testing Read-Once Polynomials

The polynomial identity testing problem, or PIT, asks how we can decide if a polynomial is equivalent to zero. A read-once polynomial (ROP) is a polynomial over some field that can be expressed with an arithmetic formula where each variable appears at most once. We construct a deterministic polynomial time algorithm for identity testing a black-box ROP. In particular, we show that for a read-once polynomial P ∈ F[x1, . . . , xn], we can decide if P ≡ 0 by plugging in nO(1) points to P . From this algorithm we can decide in polynomial time whether the sum of k ROPs is identically zero and we can re-construct a black-box ROP in polynomial time.