COUPLING POLICY ITERATION WITH SEMI-DEFINITE RELAXATION TO COMPUTE ACCURATE NUMERICAL INVARIANTS IN STATIC ANALYSIS

Abstract. We introduce a new domain for finding precise numerical invariants of pro-grams by abstract interpretation. This domain, which consists of sublevel sets of non-linear functions, generalizes the domain of linear templates introduced by Manna, Sankara-narayanan, and Sipma. In the case of quadratic templates, we use Shor’s semi-definite relaxation to derive computable yet precise abstractions of semantic functionals, and we show that the abstract fixpoint equation can be solved accurately by coupling policy it-eration and semi-definite programming. We demonstrate the interest of our approach on a series of examples (filters, integration schemes) including a degenerate one (symplectic scheme). 1