Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

Reports tagged with constant depth formulas:
TR07-031 | 26th March 2007
Yael Tauman Kalai, Ran Raz

Interactive PCP

An interactive-PCP (say, for the membership $x \in L$) is a
proof that can be verified by reading only one of its bits, with the
help of a very short interactive-proof.
We show that for membership in some languages $L$, there are
interactive-PCPs that are significantly shorter than the known
more >>>

TR18-183 | 5th November 2018
Dean Doron, Pooya Hatami, William Hoza

Near-Optimal Pseudorandom Generators for Constant-Depth Read-Once Formulas

Revisions: 2

We give an explicit pseudorandom generator (PRG) for constant-depth read-once formulas over the basis $\{\wedge, \vee, \neg\}$ with unbounded fan-in. The seed length of our PRG is $\widetilde{O}(\log(n/\varepsilon))$. Previously, PRGs with near-optimal seed length were known only for the depth-2 case (Gopalan et al. FOCS '12). For a constant depth ... more >>>

TR19-021 | 19th February 2019
Rahul Ilango

$AC^0[p]$ Lower Bounds and NP-Hardness for Variants of MCSP

The Minimum Circuit Size Problem (MCSP) asks whether a (given) Boolean function has a circuit of at most a (given) size. Despite over a half-century of study, we know relatively little about the computational complexity of MCSP. We do know that questions about the complexity of MCSP have significant ramifications ... more >>>

TR19-149 | 4th November 2019
Dean Doron, Pooya Hatami, William Hoza

Log-Seed Pseudorandom Generators via Iterated Restrictions

There are only a few known general approaches for constructing explicit pseudorandom generators (PRGs). The ``iterated restrictions'' approach, pioneered by Ajtai and Wigderson [AW89], has provided PRGs with seed length $\mathrm{polylog} n$ or even $\tilde{O}(\log n)$ for several restricted models of computation. Can this approach ever achieve the optimal seed ... more >>>

TR20-183 | 6th December 2020
Rahul Ilango

Constant Depth Formula and Partial Function Versions of MCSP are Hard

Attempts to prove the intractability of the Minimum Circuit Size Problem (MCSP) date as far back as the 1950s and are well-motivated by connections to cryptography, learning theory, and average-case complexity. In this work, we make progress, on two fronts, towards showing MCSP is intractable under worst-case assumptions.

While ... more >>>

ISSN 1433-8092 | Imprint