Predicate Abstraction and Canonical Abstraction for Singly-Linked Lists

  • Roman Manevich
  • E. Yahav
  • G. Ramalingam
  • Mooly Sagiv
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3385)

Abstract

Predicate abstraction and canonical abstraction are two finitary abstractions used to prove properties of programs. We study the relationship between these two abstractions by considering a very limited case: abstraction of (potentially cyclic) singly-linked lists.

We provide a new and rather precise family of abstractions for potentially cyclic singly-linked lists. The main observation behind this family of abstractions is that the number of shared nodes in linked lists can be statically bounded. Therefore, the number of possible “heap shapes” is also bounded. We present the new abstraction in both predicate abstraction form as well as in canonical abstraction form.

As we illustrate in the paper, given any canonical abstraction, it is possible to define a predicate abstraction that is equivalent to the canonical abstraction. However, with this straightforward simulation, the number of predicates used for the predicate abstraction is exponential in the number of predicates used by the canonical abstraction.

An important feature of the family of abstractions we present in this paper is that the predicate abstraction representation we define is far more practical as it uses a number of predicates that is quadratic in the number of predicates used by the corresponding canonical abstraction representation. In particular, for the most abstract abstraction in this family, the number of predicates used by the canonical abstraction is linear in the number of program variables, while the number of predicates used by the predicate abstraction is quadratic in the number of program variables.

We have encoded this particular predicate abstraction and corresponding transformers in TVLA, and used this implementation to successfully verify safety properties of several list manipulating programs, including programs that were not previously verified using predicate abstraction or canonical abstraction.

Keywords

Abstract State Auxiliary Variable Program Variable Concrete State Unary Predicate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Roman Manevich
    • 1
  • E. Yahav
    • 2
  • G. Ramalingam
    • 2
  • Mooly Sagiv
    • 1
  1. 1.Tel Aviv University 
  2. 2.IBM T.J. Watson Research Center 

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