Scientific publications

Since its inception as a student project in 2001, initially just for the handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library has been continuously improved and extended by joining scrupulous research on the theoretical foundations of (possibly non-convex) numerical abstractions to a total adherence to the best available practices in software development. Even though it is still not fully mature and functionally complete, the Parma Polyhedra Library already offers a combination of functionality, reliability, usability and performance that is not matched by similar, freely available libraries. In this paper, we present the main features of the current version of the library, emphasizing those that distinguish it from other similar libraries and those that are important for applications in the field of analysis and verification of hardware and software systems.

This paper explores the abstract domain of grids, a domain that is able to represent sets of equally spaced points and hyperplanes over an $n$-dimensional vector space. Such a domain is useful for the static analysis of the patterns of distribution of the values program variables can take. We present the domain, its representation and the basic operations on grids necessary to define the abstract semantics. We show how the definition of the domain and its operations exploit well-known techniques from linear algebra as well as a dual representation that allows, among other things, for a concise and efficient implementation.

The finite powerset construction upgrades an abstract domain by allowing for the representation of finite disjunctions of its elements. While most of the operations on the finite powerset abstract domain are easily obtained by ‘‘lifting’’ the corresponding operations on the base-level domain, the problem of endowing finite powersets with a provably correct widening operator is still open. In this paper we define three generic widening methodologies for the finite powerset abstract domain. The widenings are obtained by lifting any widening operator defined on the base-level abstract domain and are parametric with respect to the specification of a few additional operators that allow all the flexibility required to tune the complexity/precision trade-off. As far as we know, this is the first time that the problem of deriving non-trivial, provably correct widening operators in a domain refinement is tackled successfully. We illustrate the proposed techniques by instantiating our widening methodologies on powersets of convex polyhedra, a domain for which no non-trivial widening operator was previously known.

Sharing, an abstract domain developed by D. Jacobs and A. Langen for the analysis of logic programs, derives useful aliasing information. It is well-known that a commonly used core of techniques, such as the integration of Sharing with freeness and linearity information, can significantly improve the precision of the analysis. However, a number of other proposals for refined domain combinations have been circulating for years. One feature that is common to these proposals is that they do not seem to have undergone a thorough experimental evaluation even with respect to the expected precision gains. In this paper we experimentally evaluate: helping Sharing with the definitely ground variables found using Pos, the domain of positive Boolean formulas; the incorporation of explicit structural information; a full implementation of the reduced product of Sharing and Pos; the issue of reordering the bindings in the computation of the abstract mgu; an original proposal for the addition of a new mode recording the set of variables that are deemed to be ground or free; a refined way of using linearity to improve the analysis; the recovery of hidden information in the combination of Sharing with freeness information. Finally, we discuss the issue of whether tracking compoundness allows the computation of more sharing information.