In recent years we have seen great progress made in the area of automatic source-level static analysis tools. However, all of today’s program verification tools are limited to properties that guarantee the absence of bad events (called safety properties). Until now no formal software analysis tool has provided support for automatically proving properties that ensure that good events eventually ...

We characterise explicitly the decidable predicates on integers of Innnite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down , the least ordinal not the length of any eventual output of an Innnite Time Turing machine (halting or otherwise); using this the Innnite Time Turing Degrees are considered, and it is shown how the jump ope...

This paper is focused on the `2-induced control of eventually periodic linear discrete-time systems. We prove for such systems that a synthesis exists if and only if an eventually periodic synthesis exists. We also consider specific cases, where we show that the synthesis if existent can always be chosen to be of the same eventually periodic class as the plant. All the conditions derived are pr...

It is a well-know fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive s...

We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium x\over \tilda=1. As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one. Moreover, we show that almost all solutions of the equation are not event...

The pathophysiology of cellulite is still largely unknown. Here, we propose a new pathophysiology that connects the development of cellulite with several newly-discovered hallmarks of white adipose tissue. According to this theory, cellulite appears in hypertrophic fat tissue that is associated with overproduction of low molecular weight hyaluronan (HA). This can induce different types of fibro...