Deciding Conditional Termination

Marius Bozga (1) , Radu Iosif (1) , Filip Konecny (1, 2)

1 VERIMAG - IMAG - VERIMAG
2 FIT / BUT - Faculty of Information Technology [Brno]

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.

Domaines: Systèmes embarqués

Marius Bozga, Radu Iosif, Filip Konecny. Deciding Conditional Termination. Tools and Algorithms for the Construction and Analysis of Systems - 18th International Conference, TACAS 2012, Mar 2012, Tallinn, Estonia. pp.252-266, ⟨10.1007/978-3-642-28756-5_18⟩. ⟨hal-00722494⟩