Liqian Chen

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The polyhedra abstract domain is one of the most powerful and commonly used numerical abstract domains in the field of static program analysis based on abstract interpretation. In this paper, we present an implementation of the polyhedra domain using floating-point arithmetic without sacrificing sound-ness. Floating-point arithmetic allows a compact memory(More)
We introduce a new numerical abstract domain, so-called interval polyhedra (itvPol), to infer and propagate interval linear constraints over program variables. itvPol, which allows to represent constraints of the form k [a k , b k ]x k ≤ c, is more expressive than the classic convex polyhedra domain and allows to express certain non-convex (even(More)
We introduce a new abstract domain, namely the domain of Interval Linear Equalities (itvLinEqs), which generalizes the affine equality domain with interval coefficients by leveraging results from interval linear algebra. The representation of itvLinEqs is based on a row echelon system of interval linear equalities , which natively allows expressing(More)
Linear relation analysis (polyhedral analysis), devoted to discovering linear invariant relations among variables of a program, remains one of the most powerful abstract interpretations but is subject to convexity limitations. Absolute value enjoys piecewise linear expressiveness and thus natively fits to encode certain non-convex properties. Based on this(More)
The octagon abstract domain, devoted to discovering octagonal constraints (also called Unit Two Variable Per Inequality or UTVPI constraints) of a program, is one of the most commonly used numerical abstractions in practice, due to its quadratic memory complexity and cubic time complexity. However, the octagon domain itself is restricted to express convex(More)
One important quantitative property of CPS (Cyber-Physical Systems) software is its heap bound for which a precise analysis result needs to combine shape analysis and numeric reasoning. In this paper, we present a framework for statically finding symbolic heap bounds of CPS software. The basic idea is to separate numeric reasoning from shape analysis by(More)