Hybrid automata are a natural model for both representing and analyzing systems that exhibit a mixed discrete continuous behaviours. However, the assumption of being able of performing infinite precision measurements over them soon leads to undecidability results and, sometimes, produces evolutions that are artifacts of the model and do not correspond to any observable phenomena. A class of finite precision semantics, named -semantics, is a way to handle these problems by formally representing

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... oise, partial information, and finite precision instruments. This paper extends the classical reachability algorithm based on these semantics. Moreover, it reduces the computation of two specific -semantics to the decidability of a first-order theory and suggests how to decrease the complexity of the involved formulae. Finally, it provides two practical applications of the proposed techniques to the biological domain.