Automatic Inference of Ranking Functions by Abstract Interpretation

Caterina Urban

We present a family of parameterized abstract domains for proving termination of imperative programs by abstract interpretation. The domains automatically synthesize piecewise-defined lexicographic ranking functions and infer sufficient preconditions for program termination.

The abstract domains are parameterized by a numerical abstract domain for state partitioning and a numerical abstract domain for ranking functions. This parameterization allows to easily tune the trade-off between precision and cost of the analysis. We describe instantiations of these domains with intervals, octagons, polyhedra and affine functions.

We have implemented a prototype static analyzer for proving conditional termination of programs written in (a subset of) C and, using experimental evidence, we show that it is competitive with the state of the art and performs well on a wide variety of benchmarks.