The Stereo Event Builder (SEB) software system of the ASTRI Mini-Array is the part of the
off-line data processing chain that is responsible for identifying single and stereo Cherenkov
events. The ASTRI Mini-Array is an international project led by the Italian National Institute for
Astrophysics (INAF) which is in the process of deploying nine Imaging Atmospheric Cherenkov
Telescopes (IACTs) of the 4-m class at the Observatorio del Teide in Tenerife (Spain). The project is designed to detect very high-energy gamma rays up to the multi-TeV scale. In the ASTRI Mini-Array operation concept, the expected performance is based on the stereoscopic technique, i.e. the detection of the same atmospheric shower event with two or more telescopes. However all
single-telescope events are acquired independently and stored for off-line processing. This strong requirement must meet the need to observe muon events with each single telescope to allow for
calibrations. In this scenario, the correct identification of the single telescope triggers participating to the same stereo event is of fundamental importance. In this contribution we present the SEB constraints, design, and expected performance.