In the code static analysis, the choice of an adequate abstract domain is an interesting issue. In this paper, we provide a new numerical abstract domain: 4-Octahedron. It is an Octahedra subclass that infers relations of the form : { x ∼ α, x−y ∼ β, (x−y)−(z−t) ∼ λ}, such that: x, y, z and t are real variables, α, β and λ are real constants and ∼ ∈ {≤,≥}. The 4-Octahedron extends the conjuncti...

We propose a numerical abstract domain based on parallelotopes. A parallelotope is a polyhedron whose constraint matrix is squared and invertible. The domain of parallelotopes is a fully relational abstraction of the Cousot and Halbwachs’ polyhedra abstract domain, and does not use templates. We equip the domain of parallelotopes with all the necessary operations for the analysis of imperative ...

Static analysis by abstract interpretation [1] aims at automatically inferring properties on the behaviour of programs. We focus here on a specific kind of numerical invariants: the set of values taken by numerical variables, with a real numbers semantics, at each control point of a program. We present an implementation called Taylor1+, interfaced with the APRON library [2], of an abstract doma...

It is well known that closure operators on a complete lattice, ordered pointwise, give rise to a complete lattice, and this basic fact plays an important rôle in many fields of the semantics area, notably in domain theory and abstract interpretation. We strengthen that result by showing that closure operators on any directed-complete partial order (CPO) still form a complete lattice. An example...

The success of software model checking depends on finding an appropriate abstraction of the program to verify. The choice of the abstract domain and the analysis configuration is currently left to the user, who may not be familiar with the tradeoffs and performance details of the available abstract domains. We introduce the concept of domain types, which classify the program variables into type...

Interpretation. The semantics of a programming language can be more or less precise, depending on the degree of detail captured by the description of program execution. The framework of abstract interpretation [CC77, CC79] can be used to automatically define several semantics layers, corresponding to different levels of precision. Each semantics layer is represented by a partially ordered set, ...

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A domain representation of a topological space X is a function usually a quotient map from a subset of a domain onto X Several di erent classes of domain representations are introduced and studied It is investigated when it is possible to build domain representations from existing ones It is for example discussed whether there exists a natural way to build a domain representation of a product o...