Stasys Jukna, Stanislav Zak

We propose an information-theoretic approach to proving

lower bounds on the size of branching programs (b.p.). The argument

is based on Kraft-McMillan type inequalities for the average amount of

uncertainty about (or entropy of) a given input during various

stages of the computation. ...
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Beatrice List, Markus Maucher, Uwe SchÃ¶ning, Rainer Schuler

The worst-case complexity of an implementation of Quicksort depends

on the random number generator that is used to select the pivot

elements. In this paper we estimate the expected number of

comparisons of Quicksort as a function in the entropy of the random

source. We give upper and lower bounds ...
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Zeev Dvir, Dan Gutfreund, Guy Rothblum, Salil Vadhan

We investigate the complexity of the following computational problem:

Polynomial Entropy Approximation (PEA):

Given a low-degree polynomial mapping

$p : F^n\rightarrow F^m$, where $F$ is a finite field, approximate the output entropy

$H(p(U_n))$, where $U_n$ is the uniform distribution on $F^n$ and $H$ may be any of several entropy measures.

Salil Vadhan, Colin Jia Zheng

We provide a characterization of pseudoentropy in terms of hardness of sampling: Let $(X,B)$ be jointly distributed random variables such that $B$ takes values in a polynomial-sized set. We show that $B$ is computationally indistinguishable from a random variable of higher Shannon entropy given $X$ if and only if there ... more >>>

Venkatesan Guruswami, Patrick Xia

We prove that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within $\epsilon > 0$ of the Shannon capacity with a block length, construction complexity, and decoding complexity all bounded by a *polynomial* in $1/\epsilon$. Polar coding gives the *first known explicit construction* with rigorous ... more >>>

Salman Beigi, Omid Etesami, Amin Gohari

"Help bits" are some limited trusted information about an instance or instances of a computational problem that may reduce the computational complexity of solving that instance or instances. In this paper, we study the value of help bits in the settings of randomized and average-case complexity.

Amir, Beigel, and Gasarch ... more >>>