We consider three types of multiple input problems in the context of property testing.
Specifically, for a property $\Pi\subseteq\{0,1\}^n$, a proximity parameter $\epsilon$, and an integer $m$, we consider the following problems:

\begin{enumerate}
\item Direct $m$-Sum Problem for $\Pi$ and $\epsilon$:
Given a sequence of $m$ inputs, output a sequence ... more >>>

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(f o g^n)=Omega(R(f).R(g)) holds for a relation f in {0,1}^n * S and a total inner function g:{0,1}^m \to {0, 1}.

Let D^(prod) denote the maximum distributional query ... more >>>

We present a methodology for constructing interactive proof systems.
This methodology, which is implicit in prior works, consists of reducing the original claim to an iteratively generated sequence of claims such that each claim is (interactively) generated based on the prior claim.
Viewing each of these interactive generation ... more >>>