Efficient CTL model-checking for pushdown systems

• An efficient algorithm checking emptiness of Alternating Büchi Pushdown Systems.
• An efficient algorithm for model-checking pushdown systems (PDSs) against CTL.
• An efficient algorithm for model-checking PDSs against CTL with regular valuations.
• Implementation of these algorithms in a tool.

Pushdown systems (PDS) are well adapted to model sequential programs with (possibly recursive) procedure calls. Therefore, it is important to have efficient model checking algorithms for PDSs. We consider in this paper CTL model checking for PDSs. We consider the “standard” CTL model checking problem where whether a configuration of a PDS satisfies an atomic proposition or not depends only on the control state of the configuration. We consider also CTL model checking with regular valuations, where the set of configurations in which an atomic proposition holds is a regular language. We reduce these problems to the emptiness problem in Alternating Büchi Pushdown Systems, and we give an algorithm to solve this emptiness problem. Our algorithms are more efficient than the other existing algorithms for CTL model checking for PDSs in the literature. We implemented our techniques in a tool, and we applied it to different case studies. Our results are encouraging. In particular, we were able to confirm the existence of known bugs in Linux source code.