Tal Lev-Ami, Neil Immerman, Mooly Sagiv Abstraction for Shape Analysis with Fast and Precise Transformers, CAV '06, 533 - 546.

Abstract: This paper addresses the problem of proving safety properties of imperative programs manipulating dynamically allocated data structures using destructive pointer updates. We present a new abstraction for linked data structures whose underlying graphs do not contain cycles. The abstraction is simple and allows us to decide reachability between dynamically allocated heap cells. We present an efficient algorithm that computes the effect of low level heap mutations in the most precise way. The algorithm does not rely on the usage of a theorem prover. In particular, the worst case complexity of computing a single successor abstract state is O(V log V) where V is the number of program variables. The overall number of successor abstract states can be exponential in V . A prototype of the algorithm was implemented and is shown to be fast. Our method also handles programs with "simple cycles" such as cyclic singlylinked lists, (cyclic) doubly-linked lists, and trees with parent pointers. Moreover, we allow programs which temporarily violate these restrictions as long as they are restored in loop boundaries.