Threshold Circuits of Small Majority-Depth

Threshold Circuits of Small Majority-Depth

Constant-depth polynomial-size threshold circuits are usually classi ed according to their total depth. For example, the best known threshold circuits for iterated multiplication and division have depth four and three, respectively. In this paper, the complexity of threshold circuits is investigated from a di erent point of view: explicit AND, OR gates are allowed in the circuits, and a thresho...

On Small Depth Threshold Circuits

In this talk we will consider various classes defined by small depth polynomial size circuits which contain threshold gates and parity gates. We will describe various inclusions between many classes defined in this way and also classes whose definitions rely upon spectral properties of Boolean functions.

Separating Ac from Depth-2 Majority Circuits∗

We construct a function in AC that cannot be computed by a depth-2 majority circuit of size less than exp(Θ(n1/5)). This solves an open problem due to Krause and Pudlák (1997) and matches Allender’s classic result (1989) that AC can be efficiently simulated by depth-3 majority circuits. To obtain our result, we develop a novel technique for proving lower bounds on communication complexity. This...

Typed semigroups, majority logic, and threshold circuits

Simulating Threshold Circuits by Majority Circuits 1 (revised Version)

We prove that a single threshold gate with arbitrary weights 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, H astad, and Razborov showed in 10] that a non-uniform simulation exists. Our construction answers two open questions posed in 10]: we ...