Extending Constraint-Only Representation of Polyhedra with Boolean Constraints

  title={Extending Constraint-Only Representation of Polyhedra with Boolean Constraints},
  author={Alexey Bakhirkin and David Monniaux},
  booktitle={Sensors Applications Symposium},
We propose a new relational abstract domain for analysing programs with numeric and Boolean variables. The main idea is to represent an abstract state as a set of linear constraints over numeric variables, with every constraint being enabled by a formula over Boolean variables. This allows us, unlike in some existing approaches, to avoid duplicating linear constraints shared by multiple Boolean formulas. To perform domain operations, we adapt algorithms from constraint-only representation of… 

Modular analysis of numerical properties by abstract interpretation

A new modular analysis for the automatic discovery of numerical properties based on the computation of disjunctive relational summaries of procedures is proposed, and a flexible representation of the behavior of reactive components called Relational Mode Automata (RMA), which allows the analysis of reactive systems behavior at various levels of abstraction.

On the Monniaux Problem in Abstract Interpretation

The Monniaux Problem is undecidable for unguarded affine programs and semilinear invariants (unions of polyhedra) and it is shown that decidability is recovered in the important special case of simple linear loops.

Static Analysis: 26th International Symposium, SAS 2019, Porto, Portugal, October 8–11, 2019, Proceedings

This paper presents a corpus of invited contributions towards Semantic Adversarial Examples that describes the development of semantic adversarial models in the context of knowledge representation.



Efficient Elimination of Redundancies in Polyhedra by Raytracing

This work presents an algorithm that replaces most lp problem resolutions by distance computations and drastically reduces the number of calls to the simplex, resulting in a considerable speed improvement.

Precise widening operators for convex polyhedra

Revisiting the abstract domain of polyhedra : constraints-only representation and formal proof. (Le domaine abstrait des polyèdres revisité : représentation par contraintes et preuve formelle)

The work reported in this thesis revisits in two way the abstract domain of polyhedra used for static analysis of programs, and investigates a new approach to performing projections, based on parametric linear programming.

New Algorithmics for Polyhedral Calculus via Parametric Linear Programming. (Nouvelle Algorithmique pour le Calcul Polyédral via Programmation Linéaire Paramétrique)

This thesis presents the design and implementation of the Verified Polyhedra Library (VPL), a scalable library for polyhedral calculus. It provides Coq-certified polyhedral operators that work on

Exploiting Sparsity in Polyhedral Analysis

A projection algorithm that works directly on any sparse system of inequalities and which sacrifices precision only when necessary is presented, based on a novel combination of the Fourier-Motzkin algorithm and Simplex.

Boxes: A Symbolic Abstract Domain of Boxes

An implementation of the Boxes abstract domain - a refinement of the well-known Box (or Intervals) domain with finite disjunctions, which indicates that the performance of Boxes is superior to other existing refinements of Box with comparable expressiveness.

Cell Morphing: From Array Programs to Array-Free Horn Clauses

This work addresses the issue ofatically verifying safety properties of programs with a powerful and flexible abstraction that morphes concrete array cells into a finite set of abstract ones.

Scalable Minimizing-Operators on Polyhedra via Parametric Linear Programming

Convex polyhedra capture linear relations between variables and their high expressiveness is however barely used in verification because of their cost, often prohibitive as the number of variables involved increases.

Widening operators for powerset domains

This paper defines three generic widening methodologies for the finite powerset abstract domain and is the first time that the problem of deriving non-trivial, provably correct widening operators in a domain refinement is tackled successfully.

Using Bounded Model Checking to Focus Fixpoint Iterations

This article describes how to avoid systematic exploration in static analysis by focusing on a single path at a time, designated by SMT-solving, thus doing away with widenings as well in some cases.