Deciding Conditional Termination

Marius Bozga (1) , Radu Iosif (1) , Filip Konečny (1)

1 VERIMAG - IMAG - VERIMAG

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 quanti-fier 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: Théorie et langage formel [cs.FL]

Marius Bozga, Radu Iosif, Filip Konečny. Deciding Conditional Termination. 18th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2012), Mar 2012, Tallinn, Estonia. pp.252-266, ⟨10.1007/978-3-642-28756-5_18⟩. ⟨hal-01418906⟩