Making prophecies with decision predicates

Abstract

We describe a new algorithm for proving temporal properties expressed in LTL of infinite-state programs. Our approach takes advantage of the fact that LTL properties can often be proved more efficiently using techniques usually associated with the branching-time logic CTL than they can with native LTL algorithms. The caveat is that, in certain instances, nondeterminism in the system's transition relation can cause CTL methods to report counter examples that are spurious with respect to the original LTL formula. To address this problem we describe an algorithm that, as it attempts to apply CTL proof methods, finds and then removes problematic nondeterminism via an analysis on the potentially spurious counterexamples. Problematic nondeterminism is characterized using decision predicates , and removed using a partial, symbolic determinization procedure which introduces new prophecy variables to predict the future outcome of these choices. We demonstrate---using examples taken from the PostgreSQL database server, Apache web server, and Windows OS kernel---that our method can yield enormous performance improvements in comparison to known tools, allowing us to automatically prove properties of programs where we could not prove them before.