Deciding Conditional Termination

We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a non-terminating execution exists, as the greatest fixpoint of the function...

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Bibliographic Details
Published inLogical methods in computer science Vol. 10, Issue 3; no. 3
Main Authors Iosif, Radu, Konecny, Filip, Bozga, Marius
Format Journal Article
LanguageEnglish
Published Logical Methods in Computer Science Association 21.08.2014
Logical Methods in Computer Science e.V
Subjects
Computational Complexity
Computer Science
computer science - formal languages and automata theory
computer science - logic in computer science
Recurrent Sets
Termination Preconditions
Periodic Relations
Integer Programs
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Summary:We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a non-terminating execution exists, as the greatest fixpoint of the function that maps a set of states into its pre-image with respect to the transition relation. This definition allows to compute the weakest non-termination precondition if at least one of the following holds: (i) the transition relation is deterministic, (ii) the descending Kleene sequence overapproximating the greatest fixpoint converges in finitely many steps, or (iii) the transition relation is well founded. We show that this is the case for two classes of relations, namely octagonal and finite monoid affine relations. Moreover, since the closed forms of these relations can be defined in Presburger arithmetic, we obtain the decidability of the termination problem for such loops.
ISSN:1860-5974
1860-5974
DOI:10.2168/LMCS-10(3:8)2014