Seventh Biennial Report

ions for Shape Analysis Predicate abstraction is a method for constrained-based abstraction that has been successfully applied in many domains. Unfortunately, in the context of shape analysis it is in general not efficient enough. In [5], we describe a new approach to shape analysis based on predicate abstraction. We propose a class of state predicates that exploits existent abstractions for shape analysis [4] and uses the fact that the concrete states of the analyzed system are modeled by graphs. This makes abstractions from shape analysis usable for predicate abstraction based software model checking. We are collaborating with Martin Rinard and Viktor Kuncak from the Computer Science and Artificial Intelligence Lab at MIT and implementing a prototype of our analysis in the context of the Hob project [6]. Hob is a project that serves as a test bed to combine multiple specialized analyses for the verification of data structure consistency. There is a number of theoretical problems open for future research. Decision procedures play an important role for automatic abstraction. It is a challenging task to identify decidable fragments of logics that are expressive enough to be used for shape analysis. For shape analysis one needs second-order axioms to express properties such as reachability. An interesting question is whether it is possible to find suitable first-order approximations of these second-order axioms. This would enable the use of existing decision procedures for first-order logic in shape analysis. Abstraction refinement for shape analysis is another topic we want to further investigate. So far, in shape analysis there are no satisfying solutions to this problem.