Completeness in abstract interpretation is an ideal situation where the abstract semantics is able to take full advantage of the power of representation of the underlying abstract domain. Thus, complete abstract interpretations can be rightfully considered as optimal. In this article , we develop a general theory of completeness in abstract interpretation, also dealing with the most frequent ca...

In the context of the abstract interpretation theory, we study the relations among various abstract domains for groundness analysis of logic programs. We reconstruct the well-known domain Pos as a logical domain in a fully automatic way and we prove that it is the best abstract domain which can be set up from the property of groundness by applying logic operators only. We propose a new notion o...

interpretation theory o ers a number of methodologies that have not been applied yet in the eld of abstract model checking. A number of authors recognized in the possibility of modifying abstract models by modifying abstractions a great potential for improving abstract model checking in precision and complexity (e.g. see Section 9 in [6]), but few applications of these techniques are known in a...

3 Domain. To further test the properties of the MPA algorithm, I developed an Abstract domain with the same overall structure as the Stinger Missile domain used in the earlier experiments. States in the Abstract domain are constructed entirely of sets of literals with no variables, eliminating binding problems; the complexity in the domain instead arises in its large number of operators (approx...

We present a new numerical abstract domain for static analysis of the errors introduced by the approximation by floating-point arithmetic of real numbers computation, by abstract interpretation [3]. This work extends a former domain [4,8], with an implicitly relational domain for the approximation of the floating-point values of variables, based on affine arithmetic [2]. It allows us to analyze...

This paper contributes to a new abstract domain that combines static numeric analysis and points-to analysis. One particularity of this abstract domain lies in its high degree of modularity, in the sense that the domain is constructed by reusing its combined components as black-boxes. This modularity dramatically eases the proof of its soundness and renders its algorithm intuitive. We have prot...

Abstract The octagon abstract domain is a widely used numeric abstract domain expressing relational information between variables whilst being both computationally efficient and simple to implement. Each element of the domain is a system of constraints where each constraint takes the restricted form ̆xi ̆xj ď c. A key family of operations for the octagon domain are closure algorithms, which check...

We focus our attention on the loss of precision induced by abstract domain operations. We introduce a new technique, hints, which allows us to systematically refine the operations defined over elements of an abstract domain. We formally define hints in the abstract interpretation theory, we prove their soundness, and we characterize two families of hints: syntactic and semantic. We give some ex...

We present a new parameterized abstract domain able to refine existing numerical abstract domains with finite disjunctions. The elements of the abstract domain are decision trees where the decision nodes are labeled with linear constraints, and the leaf nodes belong to a numerical abstract domain. The abstract domain is parametric in the choice between the expressivity and the cost of the linea...