2011-2012 Seminars

A $q$-query Locally Decodable Code (LDC) is an error-correcting code that allows to read any particular symbol of the message by reading only $q$ symbols of the code word. In this talk we present a new approach for the construction of LDCs from the...

The security of several cryptosystems is based on our apparent inability to solve the following computational problem: given as input a basis B for a lattice and a target vector t , find the lattice point closest to t. This problem, referred to as...

One powerful theme in complexity theory and pseudorandomness in the past few decades has been the use of lower bounds to give pseudorandom generators (PRGs). However, the general results using this hardness vs. randomness paradigm suffer a...

Gowers' uniformity norms are defined by average of a function over specific sets of linear forms. We study norms that are similarly defined by a system of linear forms. We prove that for bounded complex functions over $F_p^n$, each such norm is...

We prove new lower bounds on the encoding length of Matching Vector (MV) codes. These recently discovered families of Locally Decodable Codes (LDCs) originate in the works of Yekhanin and Efremenko and are the only known families of LDCs with a...

It is a long-standing problem to lower bound the performance of randomized greedy algorithms for maximum matching. Aronson, Dyer, Frieze and Suen in1995 studied the modified randomized greedy (MRG) algorithm and proved that it approximates the...

We consider the problem of constructing pseudorandom generators for read-once circuits. We give an explicit construction of a pseudorandom generator for the class of read-once constant depth circuits with unbounded fan-in AND, OR, NOT and...

Shannon's notion of entropy measures the amount of "randomness" in a process. However, to an algorithm with bounded resources, the amount of randomness can appear to be very different from the Shannon entropy. Indeed, various measures of...