Simulating Threshold Circuits by Majority Circuits

We prove that a single threshold gate can be simulated by an explicit polynomial size depth 2 majority circuit. In general we show that a depth d threshold circuit can be simulated uniformly by a majority circuit of depth d+1. Goldmann, Hastad and Razborov demonstrated that a non-uniform simulation exists. Our construction answers two open questions posed in their work: We give an explicit construction whereas Goldmann, Hastad and Razborov use a randomized existence argument, and we show that such a simulation is possible even if the depth d grows with the number of variables n (the simulation in their work gives polynomial size circuits only when d is constant).

ICSI Technical Report TR-92-080

Technical Report