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 >>>

We investigate the parameterized complexity of deciding whether a constraint network is $k$-consistent. We show that, parameterized by $k$, the problem is complete for the complexity class co-W[2]. As secondary parameters we consider the maximum domain size $d$ and the maximum number $\ell$ of constraints in which a variable occurs. ... more >>>

In this paper we obtain a composition theorem that allows us to construct locally testable codes (LTCs) by repeated two-wise tensor products. This is the First composition theorem showing that repeating the two-wise tensor operation any constant number of times still results in a locally testable code, improving upon previous ... more >>>