文章基本信息

标题：Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis
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作者：Assalé Adjé ; Stéphane Gaubert ; Eric Goubault 等
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2012
卷号：8
期号：1
页码：1
DOI：10.2168/LMCS-8(1:1)2012
出版社：Technical University of Braunschweig
摘要：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).
其他关键词：abstract interpretation; policy iteration; convex programming; quadratic programming; semi-definite programming; Lyapunov functions.