@MISC{Amano_someproperties, author = {Kazuyuki Amano and Akira Maruoka}, title = {Some Properties of MODm Circuits Computing Simple Functions}, year = {} }

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Abstract

We investigate the complexity of circuits consisting solely of modulo gates and obtain results which might be helpful to derive lower bounds on circuit complexity: (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. As a consequence we might think of the strategy for deriving lower bounds on modular circuits: Suppose that a polynomial size constant depth modulo 2p circuit C computes a symmetric function. If we can show that the circuit obtained by applying the procedure given in (i) to the circuit C cannot satisfy the properties described in (ii), then we have a super-polynomial lower bound on the size of a constant depth modulo 2p circuit computing a certain symmetric function.