International audienceWhile task-based programming models allow expressing the parallelism of algorithms finely, the traditional data accesses used in the sequential task-flow model (STF) can restrict the parallelism and hide useful information. In this presentation, we describe how more precise data accesses can be used to get better performance, and how uncertain modifications of the data by the tasks open the possibility for speculative execution. We detail different speculative execution models when this uncertainty exists. We also introduce our speculative runtime system, SPETABARU, and provide examples with the parallelization of the Monte Carlo and replica exchange Monte Carlo simulations