This paper addresses the problem of conditional termination, which is that of defining the set of initial configurations from which a given program terminates. First we define the dual set, of initial configurations, from which a non-terminating execution exists, as the greatest fixpoint of the pre-image of the transition relation. This definition enables the representation of this set, whenever the closed form of the relation of the loop is definable in a logic that has quantifier elimination. This entails the decidability of the termination problem for such loops. Second, we present effective ways to compute the weakest precondition for non-termination for difference bounds and octagonal (non-deterministic) relations, by avoiding complex quantifier eliminations. We also investigate the existence of linear ranking functions for such loops. Finally, we study the class of linear affine relations and give a method of under-approximating the termination precondition for a non-trivial subclass of affine relations. We have performed preliminary experiments on transition systems modeling real-life systems, and have obtained encouraging results. © 2012 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Bozga, M., Iosif, R., & Konečný, F. (2012). Deciding conditional termination. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7214 LNCS, pp. 252–266). https://doi.org/10.1007/978-3-642-28756-5_18
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