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arXiv · 1609.05207

Geometric Nontermination Arguments

Jan Leike·Matthias Heizmann
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Abstract

We present a new kind of nontermination argument, called geometric nontermination argument. The geometric nontermination argument is a finite representation of an infinite execution that has the form of a sum of several geometric series. For so-called linear lasso programs we can decide the existence of a geometric nontermination argument using a nonlinear algebraic $\exists$-constraint. We show that a deterministic conjunctive loop program with nonnegative eigenvalues is nonterminating if an only if there exists a geometric nontermination argument. Furthermore, we present an evaluation that demonstrates that our method is feasible in practice.

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Jan Leike, Matthias Heizmann. 2016-09-16. Geometric Nontermination Arguments. https://arxiv.org/abs/1609.05207

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