"Also they are not ambitious enough. Assuming constant time arithmetic of the real numbers should get you more (like maybe even the halting problem)." Agreed.

"Also they are not ambitious enough. Assuming constant time arithmetic of the real numbers should get you more (like maybe even the halting problem)." Agreed. They do at least broach the idea though, this is from the companion paper (more theoretical): "We have thus shown that a UMM is Turing-complete, namely it can simulate any Turing machine (whether deterministic or not). Note, however, that the reverse is not necessarily true. Namely, we have not demonstrated that a UTM can simulate a UMM, or, equivalently, we have not demonstrated that a UMM is Turing-equivalent. It is worth pointing out that, if we could prove that a UMM is not Turing-equivalent, some (Turing) undecidable problems, such as the halting problem [2], may find solution within our UMM paradigm, thus contradicting the Church-Turing hypothesis [2]. Although this is an intriguing–albeit unlikely– possibility, we leave its study for future work." http://arxiv.org/pdf/1405.0931.pdf http://arxiv.org/pdf/1405.0931.pdf