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**1 - 1**of**1**### 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 ..."

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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. Key words circuit complexity, modulo gate, constant depth circuit, symmetric function, lower bound 1 Introduction To derive a strong lower bound on the size complexity in various circuit models is a big challenge in theoretical computer science. In particular, constant depth circuits are wide...