Bounded-Depth Circuits Cannot Sample Good Codes

2011 ◽  
Author(s):  
Shachar Lovett ◽  
Emanuele Viola
Keyword(s):  
Bounded Depth Circuits

scholarly journals Bounded depth circuits with weighted symmetric gates: Satisfiability, lower bounds and compression

2019 ◽  
Vol 105 ◽  
pp. 87-103
Author(s):  
Takayuki Sakai ◽  
Kazuhisa Seto ◽  
Suguru Tamaki ◽  
Junichi Teruyama
Keyword(s):  
Lower Bounds ◽  
Bounded Depth Circuits

The complexity of symmetric functions in bounded-depth circuits

1987 ◽  
Vol 25 (4) ◽  
pp. 217-219 ◽  
Author(s):  
Bettina Brustmann ◽  
Ingo Wegener
Keyword(s):  
Symmetric Functions ◽  
Bounded Depth Circuits

WEAKLY ITERATED BLOCK PRODUCTS AND APPLICATIONS TO LOGIC AND COMPLEXITY

2010 ◽  
Vol 20 (02) ◽  
pp. 319-341 ◽  
Author(s):  
HOWARD STRAUBING ◽  
PASCAL TESSON ◽  
DENIS THÉRIEN
Keyword(s):  
Wreath Product ◽  
Communication Complexity ◽  
Regular Languages ◽  
First Order ◽  
Bounded Depth Circuits ◽  
Decomposition Theorems ◽  
Block Product

Unlike the wreath product, the block product is not associative at the level of varieties. All decomposition theorems involving block products, such as the bilateral version of Krohn–Rhodes' theorem, have always assumed a right-to-left bracketing of the operands. We consider here the left-to-right bracketing, which is generally weaker. More precisely, we are interested in characterizing for any pseudovarieties of monoids U, V the smallest pseudovariety W that contains U and such that W □ V = W. This allows us to obtain new decomposition results for a number of important varieties such as DA, DO and DA * G. We apply these results to characterize the regular languages definable with generalized first-order sentences using only two variables and to shed new light on recent results on regular languages recognized by bounded-depth circuits with a linear number of wires and regular languages with small communication complexity.

scholarly journals On (Not) Computing the Möbius Function Using Bounded Depth Circuits

2012 ◽  
Vol 21 (6) ◽  
pp. 942-951 ◽  
Author(s):  
BEN GREEN
Keyword(s):  
Möbius Function ◽  
Mobius Function ◽  
Formula Group ◽  
Image Position ◽  
Bounded Depth Circuits

Any function F: {0,. . ., N − 1} → {−1,1} such that F(x) can be computed from the binary digits of x using a bounded depth circuit is orthogonal to the Möbius function μ in the sense that \[ \frac{1}{N} \sum_{0 \leq x \leq N-1} \mu(x)F(x) → 0 \quad\text{as}~~ N → \infty. \] The proof combines a result of Linial, Mansour and Nisan with techniques of Kátai and Harman, used in their work on finding primes with specified digits.

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