Synthesizing Invariants by Solving Solvable Loops

Formal program verification faces two problems. The first
problem is related to the necessity of having automated solvers that are
powerful enough to decide whether a formula holds for a set of proof obli-
gations as large as possible, whereas the second manifests in the need of
finding sufficiently strong invariants to obtain correct proof obligations.
This paper focuses on the second problem and describes a new method
for the automatic generation of loop invariants that handles polynomial
and non deterministic assignments. This technique is based on the eigen-
vector generation for a given linear transformation and on the polynomial
optimization problem, which we implemented on top of the open-source
tool Pilat.