Section: New Results

Non linear analysis: fast inference of polynomial invariants

Participants : Thomas Jensen, David Cachera, Arnaud Jobin.

We have proposed an abstract interpretation based method for inferring polynomial invariants.Our analysis uses a form of weakest precondition calculus which was already observed to be well adapted to polynomial disequality guards, and which we extend to equality guards by using parameterized polynomial division. We have shown that the choice of a suitable division operation is crucial at each iteration step in order to compute the invariant. Based on this analysis, we have designed a constraint-based algorithm for inferring polynomial invariants. We have identified heuristics to solve equality constraints between ideals, and implemented the whole analysis algorithm in Maple.A salient feature of this analysis, which distinguishes it from the approaches proposed so far in the literature, is that it does not require the use of Gröbner base computations, which are known to be costly on parameterized polynomials. Our benchmarks show that our analyzer can successfully infer invariants on a sizeable set of examples, while performing two orders of magnitude faster than other existing implementations [16] .