The existing L0 trigger requires:
\begin{itemize}
\item only one charged track (CHOD + RICH)
\item only one cluster in the calorimeter (LKr)
\item no muons: no hits in the most downstream muon veto (MUV3)
\item (optional - to be studied) no photons in the large angle vetoes (LAV)
\end{itemize}

The GPU rejection algorithm for $K^+ \rightarrow \pi^+ \pi^0$ events would join this hardware-implemented L0 trigger.
As a first step, we needed to verify:
\begin{itemize}
\item the resolution of the process of reconstructing the particle kinematic variables by means of fitting a \v{C}erenkov ring to the hits on the photomultiplier flanges;
\item the ratio between background rejection and signal acceptance: this quantity has a strong dependance on the reconstruction resolution;
\item whether the data flow and algorithm execution chain speed can be optimized in order to match the latency of the existing L0 trigger (1 \si{\milli\second}).
\end{itemize}

Since positive results from such feasibility studies were a prerequisite that must exist before the conception of the actual CUDA algorithm, a through analisys was performed by means of the NA62 software framework.

``NA62FW'', namely the NA62 software suite, is still in active development. It includes a Montecarlo event generator, featuring Geant4 modeling and event reconstruction routines for most NA62 detectors. While this thesis was developed, almost not any analisys algorithm was implemented in NA62FW. We designed the reconstruction and track propagation methods descripted in the next \chaptername~\vref{ch:reco}.