Summary: Proving Liveness by Backwards Reachability
Parosh Aziz Abdulla, Bengt Jonsson, Ahmed Rezine, and Mayank Saksena
Dept. of Information Technology, P.O. Box 337, S­751 05 Uppsala, Sweden
{parosh,bengt,rahmed,mayanks}@it.uu.se
Abstract. We present a new method for proving liveness and termination prop­
erties for fair concurrent programs, which does not rely on finding a ranking
function or on computing the transitive closure of the transition relation. The
set of states from which termination or some liveness property is guaranteed is
computed by a backwards reachability analysis. The role of ranking functions
is replaced by a check for a certain commutativity property. The method is not
complete. However, it can be seen as a complement to other methods for proving
termination, in that it transforms a termination problem into a simpler one with
a larger set of terminated states. We show the usefulness of our method by ap­
plying it to existing programs from the literature. We have also implemented it
in the framework of Regular Model Checking, and used it to automatically verify
non­starvation for parameterized algorithms.
1 Introduction
The last decade has witnessed impressive progress in the ability of tools to verify prop­
erties of hardware and software systems (e.g., [8, 14, 22]). The success has to a large
extent concerned safety properties, e.g., absence of run­time errors, deadlocks, race

Source: Abdulla, Parosh Aziz - Department of Information Technology, Uppsala Universitet

Collections: Computer Technologies and Information Sciences