Multicore processors are becoming standard called as COTS (Commercial Off The Shelf) processors but can not be fully used in the context of critical real time systems. OpenMP is one of the most used programming models to build parallel programs able to exploit such multicore processors. A lot of work try to tackle the issue of the determinism of parallel programming models. The critical real time system face an unpredictability wall of parallel programs. This paper presents Deterministic OpenMP, a new runtime for OpenMP programs, and the Little Big Processor (LBP) manycore processor design. Their aim is to help to solve the non determinism problem at the programming level but also at the execution level. When run on LBP, a Deterministic OpenMP code produces cycle by cycle deterministic computations. LBP and Deterministic OpenMP are particularly suited to safely accelerate real time embedded applications through their parallel execution.