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Journal Articles Logical Methods in Computer Science Year : 2012

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 sub-level 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 safe and computable abstractions of semantic functionals, and we show that the abstract fixpoint can be over-approximated 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).

Dates and versions

hal-00782742 , version 1 (30-01-2013)

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Cite

A. Adjé, Stéphane Gaubert, E. Goubault. Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis. Logical Methods in Computer Science, 2012, 8 (1), pp.1:01, 32. ⟨10.2168/LMCS-8(1:1)2012⟩. ⟨hal-00782742⟩
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