We study the complexity of representing polynomials as a sum of products of polynomials in few variables. More precisely, we study representations of the form $$P = \sum_{i = 1}^T \prod_{j = 1}^d Q_{ij}$$
such that each $Q_{ij}$ is an arbitrary polynomial that depends on at most $s$ variables.

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A simulation of an interactive protocol entails the use of an interactive communication to produce the output of the protocol to within a fixed statistical distance $\epsilon$. Recent works in the TCS community have propagated that the information complexity of the protocol plays a central role in characterizing the minimum ... more >>>

A recent result of Moshkovitz~\cite{Moshkovitz14} presented an ingenious method to provide a completely elementary proof of the Parallel Repetition Theorem for certain projection games via a construction called fortification. However, the construction used in \cite{Moshkovitz14} to fortify arbitrary label cover instances using an arbitrary extractor is insufficient to prove parallel ... more >>>