One death at a time

One Loop at a Time

Classic techniques for proving termination require the identification of a measure mapping program states to the elements of a well founded domain and to show that this measure decreases with each iteration of a loop in the program. This is a global termination condition — there is a single measure which must be shown to decrease over all of the loops in the program. In this abstract we look at...

One step at a time

for these devices. But the macro layer of a network can be expanded to go a long way. In the near-term, the smartphone challenge is not about providing the capacity to cope with subscriber datausage, but is related to how the signaling system is configured. To build the networks that will cope with long-term predictions requires a new approach to network construction, heterogeneous networks – m...

One organ at a time

S tem cell research—and investment into it—has been largely inspired by the hope of using stem cells to regenerate, repair or replace damaged tissue or even whole organs. Stem cell-based therapies promise to eventually solve the problems associated with conventional organ transplantation: notably tissue rejection, a shortage of donors and the poor quality of donor organs. A much improved knowle...

Proving Termination One Loop at a Time

Constructing Sequences One Step at a Time

We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain-Antichain Principle (CAC). Using this method, we are able to prove several new separations in the presence of Weak König’s Lemma (WKL), including showing that CAC ` WKL does not imply the thin set theorem for pairs, and that the principle “the product of well-quasi-orders is a wel...