For any Boolean functions $ f $ and $ g $, the question whether $ R (f\circ g)=\tilde
{\Theta}(R (f) R (g)) $, is known as the composition question for the randomized query …

Let R_eps denote randomized query complexity for error probability eps, and R:= R_ {1/3}.
In this work we investigate whether a perfect composition theorem R (fog^ n)= Omega (R (f) …

Given a Boolean function $ f:\{0, 1\}^ n\to\{0, 1\} $, the goal in the usual query model is to
compute $ f $ on an unknown input $ x\in\{0, 1\}^ n $ while minimizing the number of queries …

Direct sum theorems state that the cost of solving $ k $ instances of a problem is at least
$\Omega (k) $ times the cost of solving a single instance. We prove the first such results in …

Boolean functions are one of the central objects in the study of Computer Science. Any
decision problem can be expressed as a Boolean function that takes an $ n $-bit string as …

Search problems lie at the core of computer science. This thesis addresses two types of
search problems. The first type is local search on graphs. In this problem there is a graph G …

We study searching and sorting in rounds motivated by a fair division question: given a cake
cutting problem with $ n $ players, compute a fair allocation in at most $ k $ rounds of …