Upping the impact: to (not quite!) infinity and beyond

To Infinity and Beyond

We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, its growth blows up and is necessarily exponential. As a direct consequence, no infinite virtually nilpotent group can be generated by a bireversible Mealy automaton. The study on how (semi)groups grow has been highlighted since Milnor’s question on the existence of groups of intermediate...

To Infinity and Beyond

Computer algebra systems (CAS) are sometimes expected to compute with infinities symbolically. Since operations on such objects do not always conform to a sufficient and consistent set of rules for ordinary arithmetic, some compromises are necessary. We discuss a few options and implementations.

To infinity, and beyond!

Charm and Anticharm—Not Quite the Same

From what we can observe, there is no symmetry between matter and antimatter in the Universe. All structures, from unimaginably large clusters of galaxies to microscopic human cells, are made of matter: protons, neutrons, and electrons. Though it is possible to produce antimatter—antiprotons, antineutrons, and positrons—in high-energy particle collisions, and even make medical use of positrons,...

Translating Uppaal to Not Quite C*

This project presents a simple translation from Uppaal models of real-time controllers to NQC programs. The modeling of these controllers in Uppaal provides a way to verify the requirements on these controllers. The user directs the translation by defining a type for each variable used in the model and by assigning each automaton in the model to a controller. The translation, that has been impl...