Some Properties of Modulo m Circuit Computing Simple Functions

In this note, we investigate the complexity of circuits with modulo gates only in two ways. (i) We describe a procedure that converts a circuit with only modulo 2p gates, where p is a prime number, into a depth two circuit with modulo 2 gates at the input level and a modulo p gate at the output. (ii) We show some properties of such depth two circuits computing symmetric functions. Thus if we can show that, for any linear size constant depth modulo 6 circuit C, a circuit obtained from C by the procedure described in (i) can not satisfy the properties described in (ii), then we could have a superlinear lower bound on the size of a constant depth modulo 6 circuit computing some symmetric functions.