On verifying complex properties using symbolic shape analysis

One of the main challenges in the verification of software systems is the analysis of unbounded data structures with dynamic memory allocation such as linked data structures and arrays. We describe Bohne a new analysis for verifying data structures. Bohne verifies data structure operations and shows that 1) the operations preserve data structure invariants and 2) the operations satisfy their specifications expressed in terms of changes to the set of objects stored in the data structure. During the analysis Bohne infers loop invariants in the form of disjunctions of universally quantified Boolean combinations of formulas represented as sets of binary decision diagrams. To synthesize loop invariants of this form Bohne uses a combination of decision procedures for Monadic Second-Order Logic over trees SMT-LIB decision procedures (currently CVC Lite) and an automated reasoner within the Isabelle interactive theorem prover. This architecture shows that synthesized loop invariants can serve as a useful communication mechanism between different decision procedures. In addition Bohne uses field constraint analysis a combination mechanism that enables the use of uninterpreted function symbols within formulas of Monadic Second-Order Logic over trees. Using Bohne we have verified operations on data structures such as linked lists with iterators and back pointers trees with and without parent pointers two-level skip lists array data structures and sorted lists. We have deployed Bohne in the Hob and Jahob data structure analysis systems enabling us to combine Bohne with analyses of data structure clients and apply it in the context of larger programs. This report describes the Bohne algorithm as well as techniques that Bohne uses to reduce the ammount of annotations and the running time of the analysis