A relational shape abstract domain

A Relational Shape Abstract Domain

Static analyses aim at inferring semantic properties of programs. While many analyses compute an over-approximation of reachable states, some analyses compute a description of the input-output relations of programs. In the case of numeric programs, several analyses have been proposed that utilize relational numerical abstract domains to describe relations. On the other hand, designing abstracti...

Relational Abstract Domain of Weighted Hexagons

We propose a new numerical abstract domain for static analysis by abstract interpretation, the domain of Weighted Hexagons. It is capable of expressing interval constraints and relational invariants of the form x ≤ a · y, where x and y are variables and a denotes a non-negative constant. This kind of domain is useful in analysis of safety for array accesses when multiplication is used (e.g. in ...

Relational System Theory Abstract

A Time-Domain Method for Shape Reconstruction of a Target with Known Electrical Properties (RESEARCH NOTE)

This paper uses a method for shape reconstruction of a 2-D homogeneous object with arbitrary geometry and known electrical properties. In this method, the object is illuminated by a Gaussian pulse, modulated with sinusoidal carrier plane wave and the time domains’ footprint signal due to object presence is used for the shape reconstruction. A nonlinear feedback loop is used to minimize the diff...

Weakly Relational Numerical Abstract Domains

Interpretation Abstract Interpretation: General theory of sound approximations of semantics [Cousot78]. Numerical Abstract Domain: • computer-representable set D of abstract values, together with: • a concretisation: γ: D → P(V → I), • a partial order: ⊑, ⊥, ⊤, • sound, effective abstract transfer functions {| I |}: ({| I |} ◦ γ)(X ) ⊆ (γ ◦ {| I |})(X ), a sound, effective abstract union ∪: γ(X...