Publication Details

Deciding Conditional Termination

KONEČNÝ Filip, IOSIF Radu and BOZGA Marius. Deciding Conditional Termination. Lecture Notes in Computer Science, vol. 2012, no. 7214, pp. 252-266. ISSN 0302-9743.
Czech title
Rozhodování podmíněné konečnosti
journal article
Konečný Filip, Ing. (DITS FIT BUT)
Iosif Radu (VERIMAG)
Bozga Marius (VERIMAG)

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


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.

Lecture Notes in Computer Science, vol. 2012, no. 7214, ISSN 0302-9743
Springer Verlag
   author = "Filip Kone\v{c}n\'{y} and Radu Iosif and Marius Bozga",
   title = "Deciding Conditional Termination",
   pages = "252--266",
   journal = "Lecture Notes in Computer Science",
   volume = 2012,
   number = 7214,
   year = 2012,
   ISSN = "0302-9743",
   language = "english",
   url = ""
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