Pushed by economical and ecological stakes, embedded systems from the avionics, automotive and automation domains, featuring real-time, safety and critical capabilities have to face increasing performance needs that will no more be satisfied by existing architectures based on single-cores. Current trends are to take benefit from multi-core processors high performance in replacing single-cores by multi-cores which raises predictability and isolation challenges for timing and mixed criticality aspects. This is mainly due to the inadequateness and inability of current approaches to effectively handle reliability and the cause of non-deterministic behaviour on multi-cores.Facing multi-core architectures' inevitable use, CERTAINTY will introduce a disruptive methodology for the design of complex critical applications allowing safety and time criticality aspects composition, taking into account unpredictability of shared resource availability as elements of the problem space, identify analysis methods and techniques supporting this new approach and demonstrate the applicability of these techniques through meaningful examples of complex control functions.New methodology and design tools, applicable in diverse industrial sectors, will be validated in an avionics application on a multi-core architecture: an existing Flight Management System will be analyzed using the CERTAINTY Methodology and Analysis Tools to specify which part could be at which critical level redesigned and composed according to the methodology. The system design will be evaluated to show that relevant safety requirements are met (i.e. ability to ensure partitioning/isolation, ability to provide a WCET, system determinism and incrementality), contributing to the certification process on new architecture generations. The major result will be a Proof of Concept of a design methodology, resultant Analysis Methodologies and associated synthesis tools: CERTAINTY Methodology and prototypes.The impact of CERTAINTY will be to contribute to the certification of mixed criticality applications on multi cores in more efficient and effective ways (performance improvement regarding strict temporal partitioning), and provide recommendations to standardization working groups preparing the way for new standards in this area.