Some lower bounds in parameterized AC0

Some Lower Bounds in Parameterized AC^0

We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical AC0. Among others, we derive such a lower bound for all fptapproximations of the parameterized clique problem and for a parameterized halting problem, which recently turned out to link problems of computational complexity, descriptive complexity, and proof theory. To show the fir...

Some lower bounds in parameterized ${\rm AC}^0$

We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical AC. Among others, we derive such a lower bound for all fptapproximations of the parameterized clique problem and for a parameterized halting problem, which recently turned out to link problems of computational complexity, descriptive complexity, and proof theory. To show the firs...

18.405J S16 Lecture 6: AC0 Lower Bounds and Switching Lemma

The key ingredient is the so-called Switching Lemma. To state it we need a notion of p-restrictions. Say we have a function f : {0, 1}n → {0, 1}. Then we say that a function f ′ is a p-restriction of f , if it is obtained from f via the following process. Each variable is set to zero with probability (1− p)/2, and is set to one with the same probability (so, with probability p a variable is not...

Some Lower Bounds for Estrada Index

Learning and Lower Bounds for AC0 with Threshold Gates

In 2002 Jackson et al. [JKS02] asked whether AC circuits augmented with a threshold gate at the output can be efficiently learned from uniform random examples. We answer this question affirmatively by showing that such circuits have fairly strong Fourier concentration; hence the low-degree algorithm of Linial, Mansour and Nisan [LMN93] learns such circuits in sub-exponential time. Under a conje...