Section: New Results

The correctness of program using finite precision

Participants : Ivan Gazeau, Dale Miller.

Programs dealing with real number quantities must live with the fact that such numbers are represented using only finite precision. As such, programs that might be considered correct over the abstract field of infinite precision arithmetic can display chaotic and incorrect behaviors when run on actual computer hardware.

One such problem with finite precision is that programs can “leak” information about values that are intended to be hidden or at least obfuscated as happens in the area differential privacy. In [22] , Gazeau, Miller, and Palamidessi illustrated just how such attacks on information hiding can be made and how it is possible to add noise to reported data values in such a way that only appropriate amounts of information leakage occurs.

In his PhD thesis, Safe Programming in finite precision: Controlling the errors and information leaks (École Polytechnique, 2013 [11] ), Gazeau develops that theme further as well as shows how techniques from rewriting theory can be applied to show that, in some situations, the chaotic behavior of finite precision programs can be expected to converge in acceptable time to acceptable answers.