Team abstraction

Overall Objectives
Scientific Foundations
Application Domains
New Results
Contracts and Grants with Industry
Other Grants and Activities

Section: New Results

Combining Abstractions

Logical Abstract Domains and Interpretations

Participants : Patrick Cousot, Radhia Cousot, Laurent Mauborgne [IMDEA Software (Madrid, Spain)] .

In [33] , we give semantic foundations to abstract domains consisting in first order logic formulæ in a theory, as used in verification tools or methods using SMT-solvers or theorem provers. We exhibit conditions for a sound usage of such methods with respect to multi-interpreted semantics and extend their usage to automatic invariant generation by abstract interpretation.

A Framework for Combining Algebraic and Logical Abstract Interpretations

Participants : Patrick Cousot, Radhia Cousot, Laurent Mauborgne [IMDEA Software (Madrid, Spain)] .

In [38] , [35] , we have introduced a reduced product combining algebraic and logical abstractions to design program correctness verifiers and static analyzers by abstract interpretation. The key new idea is to show that the Nelson-Oppen procedure for combining theories in SMT-solvers computes a reduced product in an observational semantics, so that algebraic and logical abstract interpretations can naturally be combined in a classical way using a reduced product on this observational semantics. The main practical benefit is that reductions can be performed within the logical abstract domains, within the algebraic abstract domains, and also between the logical and the algebraic abstract domains, including the case of abstractions evolving during the analysis.

Extrapolation operators for combinations of abstract domains

Participants : Agostino Cortesi [Università Ca'Foscardi di Venizia] , Matteo Zanioli.

Extrapolation operators are crucial to ensure the scalability of the analysis to large software systems. In [12] , we set the ground for a systematic design of widening and narrowing operators, by comparing the different definitions introduced in the literature and by discussing how to tune them in case of domain abstraction and domains’ combination through cartesian and reduced products.


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