Static analysis of list-manipulating programs via bit-vectors and numerical abstractions

  • Authors:

  • Liqian Chen;Renjian Li;Xueguang Wu;Ji Wang

  • Affiliations:

  • National University of Defense Technology, Changsha, China and National Laboratory for Parallel and Distributed Processing, Changsha, China;National University of Defense Technology, Changsha, China;National University of Defense Technology, Changsha, China;National University of Defense Technology, Changsha, China and National Laboratory for Parallel and Distributed Processing, Changsha, China

  • Venue:
  • Proceedings of the 28th Annual ACM Symposium on Applied Computing
  • Year:
  • 2013

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Abstract

We present an approach under the framework of abstract interpretation to analyze list-manipulating programs by combining shape and numerical abstractions. The analysis automatically divides a list into non-overlapping list segments according to the reachability property of pointer variables to list nodes. The list nodes in each segment are abstracted by a bit-vector wherein each bit corresponds to a pointer variable and indicates whether the nodes can be reached by that pointer variable. Moreover, for each bit-vector, we introduce an auxiliary integer variable, namely a counter variable, to record the number of nodes in the segment abstracted by that bit-vector. On this basis, we leverage the power of numerical abstractions to discover numerical relations among counter variables, so as to infer relational length properties among list segments. Our approach stands out in its ability to find intricate properties that involve both shape and numerical information, which are important for checking program properties such as memory safety and termination. A prototype is implemented and preliminary experimental results are encouraging.