Geometric Series as Nontermination Arguments for Linear Lasso Programs

Abstract

We present a new kind of nontermination argument for linear lasso programs, called geometric nontermination argument. A geometric nontermination argument is a finite representation of an infinite execution of the form $(\vec{x}+{\sum }_{i=0}^t{\lambda }^i\vec{y}{)}_{t\ge 0}$. The existence of this nontermination argument can be stated as a set of nonlinear algebraic constraints. We show that every linear loop program that has a bounded infinite execution also has a geometric nontermination argument. Furthermore, we discuss nonterminating programs that do not have a geometric nontermination argument.

WST 2014