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

@inproceedings{Adj2010CouplingPI, 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.}, year={2010} }

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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