Assertion checking over combined abstraction of linear arithmetic and uninterpreted functions

Sumit Gulwani and Ashish Tiwari

Presented at ESOP 2006, Vienna, Austria, Mar 27-28, 2006. Springer-Verlag. The final version will appear at the the Springer LNCS site.

Abstract

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.

pdf. or Springer link to the paper.

Slides

In powerpoint: ppt

BibTeX Entry


@inproceedings{GulwaniTiwari06:ESOP,
	author = "S. Gulwani and A. Tiwari",
	title = "Assertion checking over combined abstraction of linear arithmetic and uninterpreted functions",
	booktitle = {European Symp. on Programming, ESOP 2006},
	year = 2006,
	editor = "P. Sestoft",
	series = {LNCS},
	volume = 3924,
	pages = "279--293",
}


Return to the Ashish's home page
Return to the Computer Science Laboratory home page