Adjé, Assalé and Gaubert, Stéphane and Goubault, Eric - Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis

lmcs:687 - Logical Methods in Computer Science, January 19, 2012, Volume 8, Issue 1
Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis

Authors: Adjé, Assalé and Gaubert, Stéphane and Goubault, Eric

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).


Source : oai:arXiv.org:1111.5223
DOI : 10.2168/LMCS-8(1:1)2012
Volume: Volume 8, Issue 1
Published on: January 19, 2012
Submitted on: June 11, 2010
Keywords: Computer Science - Logic in Computer Science,Mathematics - Optimization and Control


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