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arXiv · 1405.4413

Geometric Series as Nontermination Arguments for Linear Lasso Programs

Jan Leike·Matthias Heizmann
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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 $(\vec{x} + \sum_{i=0}^t λ^i \vec{y})_{t \geq 0}$. 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.

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Jan Leike, Matthias Heizmann. 2014-05-17. Geometric Series as Nontermination Arguments for Linear Lasso Programs. https://arxiv.org/abs/1405.4413

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