Finding Recurrent Sets with Backward Analysis and Trace Partitioning

We propose an abstract-interpretation-based analysis for recurrent sets. A recurrent set is a set of states from which the execution of a program cannot or might not (as in our case) escape. A recurrent set is a part of a program’s nontermination proof (that needs to be complemented by reachability analysis). We find recurrent sets by performing a potentially over-approximate backward analysis that produces an initial candidate. We then perform over-approximate forward analysis on the candidate to check and refine it and ensure soundness. In practice, the analysis relies on trace partitioning that predicts future paths through the program that non-terminating executions will take. Using our technique, we were able to find recurrent sets in many benchmarks found in the literature including some that, to our knowledge, cannot be handled by existing tools. In addition, we note that typically, analyses that search for recurrent sets are applied to linear under-approximations of programs or employ some form of non-approximate numeric reasoning. In contrast, our analysis uses standard abstract-interpretation techniques and is potentially applicable to a larger class of abstract domains (and therefore – programs).