Dynamic Shape Analysis Using Spectral Graph Properties

Dynamically allocated data structures pervade imperative and object-oriented programs. Automated analysis and testing of such programs requires reasoning about their data structures. The structures often have complex structural properties, such as a cyclicity of the object graph rooted at a given pointer. Such properties pose a challenge for automated reasoning. Shape analysis is a class of techniques that address reasoning about such programs. Traditionally, shape analysis is performed using static analysis of the program code. More recently, dynamic techniques for shape analysis have been developed, which inspect program states to identify properties of data structures. This paper presents a novel dynamic technique, which adapts well-studied results from graph theory to determine the shape of the program's key data structures. Specifically, spectral graph theory, a field that studies the properties of a graph in relation to the properties of matrices based on the graph, e.g., eigen values of its adjacency matrix, provides the foundational ideas. Experimental results using a suite of data structures demonstrate the potential the technique holds in identifying data structure properties and detecting likely erroneous program states.