O-Minimal Invariants for Linear Loops

The termination analysis of linear loops plays a key role in several areas of computer science, including program verification and abstract interpretation.

Such deceptively simple questions also relate to a number of deep open problems, such as the decidability of the Skolem and Positivity Problems for linear recurrence sequences, or equivalently reachability questions for discrete-time linear dynamical systems.

In this talk, based on our recent ICALP papear, we introduce the class of o-minimal invariants, which is broader than any previously considered, and study the decidability of the existence and algorithmic synthesis of such invariants as certificates of non-termination for linear loops equipped with a large class of halting conditions.

We establish two main decidability results, one of them conditional on Schanuel's conjecture in transcendental number theory. 

This is joint work with Dmitry Chistikov, Joël Ouaknine, and James Worrell