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arXiv · 1111.5223

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

Assalé Adjé·Stéphane Gaubert·Eric Goubault
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Abstract

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).

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Assalé Adjé, Stéphane Gaubert, Eric Goubault. 2011-11-22. Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis. https://doi.org/10.2168/lmcs-8(1:1)2012

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