Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis

  title={Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis},
  author={Assal{\'e} Adj{\'e} and St{\'e}phane Gaubert and {\'E}ric Goubault},
  booktitle={Log. Methods Comput. Sci.},
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… 
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