Leaping loops in the presence of abstraction

Thomas Ball*, Orna Kupferman, Mooly Sagiv

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

15 Scopus citations


Finite abstraction helps program analysis cope with the huge state space of programs. We wish to use abstraction in the process of error detection. Such a detection involves reachability analysis of the program. Reachability in an abstraction that under-approximates the program implies reachability in the concrete system. Under-approximation techniques, however, lose precision in the presence of loops, and cannot detect their termination. This causes reachability analysis that is done with respect to an abstraction to miss states of the program that are reachable via loops. Current solutions to this loop-termination challenge are based on fair termination and involve the use of well-founded sets and ranking functions. In many cases, the concrete system has a huge, but still finite set of states. Our contribution is to show how, in such cases, it is possible to analyze termination of loops without refinement and wimout well-founded sets and ranking functions. Instead, our method is based on conditions on the structure of the graph that corresponds to the concrete system - conditions that can be checked with respect to the abstraction. We describe our method, demonstrate its usefulness and show how its application can be automated by means of a theorem prover.

Original languageAmerican English
Title of host publicationComputer Aided Verification - 19th International Conference, CAV 2007, Proceedings
PublisherSpringer Verlag
Number of pages13
ISBN (Print)3540733671, 9783540733676
StatePublished - 2007
Event19th International Conference on Computer Aided Verification, CAV 2007 - Berlin, Germany
Duration: 3 Jul 20077 Jul 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4590 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Computer Aided Verification, CAV 2007


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