Zero-one permanent is not=P-complete, a simpler proof

Valiant (1979) proved that computing the permanent of a 01-matrix is not=P-complete. The authors present another proof for the same result. The proof uses 'black box' methodology, which facilitates its presentation. They also prove that deciding whether the permanent is divisible by a small prime is not=P-hard. They conclude by proving that a polynomially bounded function can not be not=P-complete under 'reasonable' complexity assumptions.<>