We introduce a fragment of separation logic, called NOLL, for auto- mated reasoning about programs manipulating overlaid and nested linked lists, where overlaid means that the lists may share the same set of objects. The dis- tinguishing features of NOLL are: (1) it is parametrized by a set of user-defined predicates specifying nested linked list segments, (2) a "per-field" version of the separating conjunction allowing to share locations but not fields, and (3) it can express sharing constraints between list segments. We prove that checking the entailment between two NOLL formulas is co-NP complete. For this result, the decision procedure for entailment is based on a small model property. We also provide an effective procedure for checking entailment in NOLL, which first con- structs a Boolean abstraction of the two formulas, in order to infer all the implicit constraints, and then, it checks the existence of a homomorphism between the two formulas, viewed as graphs. We have implemented this procedure and ap- plied it on verification conditions generated from several interesting case studies that manipulate overlaid and nested data structures.
