Assertion Checking over Combined Abstraction of Linear Arithmetic and Uninterpreted Functions

  • Sumit Gulwani
  • Ashish Tiwari
Conference paper

DOI: 10.1007/11693024_19

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3924)
Cite this paper as:
Gulwani S., Tiwari A. (2006) Assertion Checking over Combined Abstraction of Linear Arithmetic and Uninterpreted Functions. In: Sestoft P. (eds) Programming Languages and Systems. ESOP 2006. Lecture Notes in Computer Science, vol 3924. Springer, Berlin, Heidelberg


This paper presents results on the problem of checking equality assertions in programs whose expressions have been abstracted using combination of linear arithmetic and uninterpreted functions, and whose conditionals are treated as non-deterministic.

We first show that the problem of assertion checking for this combined abstraction is coNP-hard, even for loop-free programs. This result is quite surprising since assertion checking for the individual abstractions of linear arithmetic and uninterpreted functions can be performed efficiently in polynomial time.

Next, we give an assertion checking algorithm for this combined abstraction, thereby proving decidability of this problem despite the underlying lattice having infinite height. Our algorithm is based on an important connection between unification theory and program analysis. Specifically, we show that weakest preconditions can be strengthened by replacing equalities by their unifiers, without losing any precision, during backward analysis of programs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sumit Gulwani
    • 1
  • Ashish Tiwari
    • 2
  1. 1.Microsoft ResearchRedmondUSA
  2. 2.SRI InternationalMenlo ParkUSA

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