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Electronic Colloquium on Computational Complexity

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Reports tagged with threshold circuit:
TR97-002 | 28th January 1997
Richard Beigel, Alexis Maciel

Upper and Lower Bounds for Some Depth-3 Circuit Classes

We investigate the complexity of depth-3 threshold circuits
with majority gates at the output, possibly negated AND
gates at level two, and MODm gates at level one. We show
that the fan-in of the AND gates can be reduced to O(log n)
in the case where ... more >>>

TR97-016 | 29th April 1997
Manindra Agrawal, Eric Allender, Samir Datta

On TC^0, AC^0, and Arithmetic Circuits

Continuing a line of investigation that has studied the
function classes #P, #SAC^1, #L, and #NC^1, we study the
class of functions #AC^0. One way to define #AC^0 is as the
class of functions computed by constant-depth polynomial-size
arithmetic circuits of unbounded fan-in addition ... more >>>

TR04-090 | 3rd November 2004
Kazuyuki Amano, Akira Maruoka

Better Simulation of Exponential Threshold Weights by Polynomial Weights

We give an explicit construction of depth two threshold circuit with polynomial weights and $\tilde{O}(n^5)$ gates that computes an arbitrary threshold function. We also give the construction of such circuits with $O(n^3/\log n)$ gates computing the COMPARISON and CARRY functions, and that with $O(n^4/\log n)$ gates computing the ADDITION function. ... more >>>

TR18-143 | 16th August 2018
Mark Bun, Justin Thaler

The Large-Error Approximate Degree of AC$^0$

We prove two new results about the inability of low-degree polynomials to uniformly approximate constant-depth circuits, even to slightly-better-than-trivial error. First, we prove a tight $\tilde{\Omega}(n^{1/2})$ lower bound on the threshold degree of the Surjectivity function on $n$ variables. This matches the best known threshold degree bound for any AC$^0$ ... more >>>

TR21-002 | 8th January 2021
Pooya Hatami, William Hoza, Avishay Tal, Roei Tell

Fooling Constant-Depth Threshold Circuits

Revisions: 1

We present new constructions of pseudorandom generators (PRGs) for two of the most widely-studied non-uniform circuit classes in complexity theory. Our main result is a construction of the first non-trivial PRG for linear threshold (LTF) circuits of arbitrary constant depth and super-linear size. This PRG fools circuits with depth $d\in\mathbb{N}$ ... more >>>

TR21-125 | 23rd August 2021
Zhiyuan Fan, Jiatu Li, Tianqi Yang

The Exact Complexity of Pseudorandom Functions and Tight Barriers to Lower Bound Proofs

How much computational resource do we need for cryptography? This is an important question of both theoretical and practical interests. In this paper, we study the problem on pseudorandom functions (PRFs) in the context of circuit complexity. Perhaps surprisingly, we prove extremely tight upper and lower bounds in various circuit ... more >>>

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