Coupling policy iteration with semi-definite relaxation to compute   accurate numerical invariants in static analysis
  We introduce a new domain for finding precise numerical invariants of programs by abstract interpretation. This domain, which consists of level sets of non-linear functions, generalizes the domain of linear "templates" introduced by Manna, Sankaranarayanan, 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 iteration 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). 
Assal\'e Adj\'e (LIX, Ecole Polytechnique, and CEA LIST), St\'ephane   Gaubert (INRIA Saclay, and Ecole Polytechnique), Eric...
cs.LO math.OC