Undecidability over Continuous Time

Since 1996, some models of recursive functions over the real numbers have been analyzed by several researchers. It could be expected that they exhibit a computational power much greater than that of Turing machines (as other well known models of computation over the real numbers already considered in the past fifteen years, like neural net models with real weights). The fact is that they have not got such a power. Although they decide the classical halting problem of Turing machines, they have almost the same limitations of Turing machines. Our profit on them has been to represent classical complexity classes (like P or NP ) by analytical means, and possibly relate them by unusual