Abstract
The concept of {\sl compactor} has been introduced in [{\em Eun Jung Kim, Maria J. Serna, and Dimitrios M. Thilikos. Data-compression for parametrized counting problems on sparse graphs. ISAAC 2018, LIPIcs Vol. 123:20:1–20:13\,}] as a general data-reduction concept for param\-etrized counting problems.For a function $F:\Sigma^*\to \Bbb{N}$ and a parameterization $\kappa: \Sigma^*\to \Bbb{N}$, a compactor $({\sf C},{\sf E})$ consists of a polynomial-time computable function ${\sf P}$, called \emph{condenser}, and a computable function ${\sf M}$, called \emph{extractor}, such that $F={\sf M}\circ {\sf P}$.If the size of ${\sf P}(x)$ is bounded by a polynomial function of $\kappa(x)$, then we say that that the compactor $({\sf C},{\sf E})$ is of polynomial size. Compactors can be seen as an attempt to formalize the notion of preprocessing for counting problems.