In this paper we construct a cyclically invariant Boolean function
whose sensitivity is $\Theta(n^{1/3})$. This result answers two
previously published questions. Tur\'an (1984) asked if any
Boolean function, invariant under some transitive group of
permutations, has sensitivity $\Omega(\sqrt{n})$. Kenyon and Kutin
(2004) asked whether for a ``nice'' function the product ... more >>>

An error-correcting code is said to be {\em locally testable} if it has an
efficient spot-checking procedure that can distinguish codewords
from strings that are far from every codeword, looking at very few
locations of the input in doing so. Locally testable codes (LTCs) have
generated ... more >>>

The notion of promise problems was introduced and initially studied
by Even, Selman and Yacobi
(Information and Control, Vol.~61, pages 159-173, 1984).
In this article we survey some of the applications that this
notion has found in the twenty years that elapsed.
These include the notion ... more >>>