Deciding Conditional Termination

Deciding Conditional Termination

Peer-reviewed article not indexed in WoS or Scopus

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.

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.

termination problem, conditional termination problem, difference bounds relations, octagonal relations, finite monoid affine relations

termination problem, conditional termination problem, difference bounds relations, octagonal relations, finite monoid affine relations

KONEČNÝ, F.; IOSIF, R.; BOZGA, M.

2013

01.04.2012

0302-9743

Lecture Notes in Computer Science

2012

7214

Federal Republic of Germany

252

266

16