The superposition (or composition) problem is a problem of
representation of a function $f$ by a superposition of "simpler" (in a
different meanings) set $\Omega$ of functions. In terms of circuits
theory this means a possibility of computing $f$ by a finite circuit
with 1 fan-out gates $\Omega$ of functions.

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The main result of this paper is a simple, yet generic, composition theorem for low error two-query probabilistically checkable proofs (PCPs). Prior to this work, composition of PCPs was well-understood only in the constant error regime. Existing composition methods in the low error regime were non-modular (i.e., very much tailored ... more >>>

We introduce a new form of composition called \emph{weak composition} that allows us to obtain polynomial kernelization lower-bounds for several natural parameterized problems. Let $d \ge 2$ be some constant and let $L_1, L_2 \subseteq \{0,1\}^* \times \N$ be two parameterized problems where the unparameterized version of $L_1$ is \NP-hard. ... more >>>