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Electronic Colloquium on Computational Complexity

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Reports tagged with Circuit Complexity Lower Bounds:
TR99-010 | 1st April 1999
Eric Allender, Igor E. Shparlinski, Michael Saks

A Lower Bound for Primality

Comments: 1

Recent work by Bernasconi, Damm and Shparlinski
proved lower bounds on the circuit complexity of the square-free
numbers, and raised as an open question if similar (or stronger)
lower bounds could be proved for the set of prime numbers. In
this short note, we answer this question ... more >>>

TR17-149 | 7th October 2017
Or Meir, Avi Wigderson

Prediction from Partial Information and Hindsight, with Application to Circuit Lower Bounds

Revisions: 5

Consider a random sequence of $n$ bits that has entropy at least $n-k$, where $k\ll n$. A commonly used observation is that an average coordinate of this random sequence is close to being uniformly distributed, that is, the coordinate “looks random”. In this work, we prove a stronger result that ... more >>>

TR17-190 | 6th November 2017
Anirbit Mukherjee, Amitabh Basu

Lower bounds over Boolean inputs for deep neural networks with ReLU gates.

Motivated by the resurgence of neural networks in being able to solve complex learning tasks we undertake a study of high depth networks using ReLU gates which implement the function $x \mapsto \max\{0,x\}$. We try to understand the role of depth in such neural networks by showing size lowerbounds against ... more >>>

TR17-191 | 15th December 2017
Alexander Smal, Navid Talebanfard

Prediction from Partial Information and Hindsight, an Alternative Proof

Revisions: 2

Let $X$ be a random variable distributed over $n$-bit strings with $H(X) \ge n - k$, where $k \ll n$. Using subadditivity we know that a random coordinate looks random. Meir and Wigderson [TR17-149] showed a random coordinate looks random to an adversary who is allowed to query around $n/k$ ... more >>>

TR18-076 | 22nd April 2018
Abhishek Bhrushundi, Kaave Hosseini, Shachar Lovett, Sankeerth Rao

Torus polynomials: an algebraic approach to ACC lower bounds

Revisions: 2

We propose an algebraic approach to proving circuit lower bounds for ACC0 by defining and studying the notion of torus polynomials. We show how currently known polynomial-based approximation results for AC0 and ACC0 can be reformulated in this framework, implying that ACC0 can be approximated by low-degree torus polynomials. Furthermore, ... more >>>

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