SPLASH Workshops 2020
2020 ACM SIGPLAN International Conference on Systems, Programming, Languages, and Applications: Software for Humanity (SPLASH Workshops 2020)
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9th ACM SIGPLAN International Workshop on Numerical and Symbolic Abstract Domains (NSAD 2020), November 17, 2020, Virtual, USA

NSAD 2020 – Preliminary Table of Contents

Contents - Abstracts - Authors

9th ACM SIGPLAN International Workshop on Numerical and Symbolic Abstract Domains (NSAD 2020)


Title Page

Message from the Chairs
Welcome to the Ninth International Workshop on Numerical and Symbolic Abstract Domains (NSAD 2020). The workshop took place virtually (online) on November 17, 2020 as a satellite event to the  ACM SIGPLAN conference on Systems, Programming, Languages, and Applications: Software for Humanity (SPLASH 2020).

Invited Talk

Abstract Domains in SMT Solving for Real Algebra (Invited Talk)
Erika Abraham
(RWTH Aachen University, Germany)

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Abstract Domains for Constraint Programming with Differential Equations
Ghiles Ziat, Olivier Mullier, Julien Alexandre dit Sandretto, Christophe Garion, Alexandre Chapoutot, and Xavier Thirioux
(ISAE-supaero, France; ENSTA Paris, France)
Cyber-physical systems (CPSs), as cruise control systems, involve life-critical or mission critical functions that must be validated. Formal verification techniques can bring high assurance level but have to be extended to embrace all the components of CPSs. Physical part models of CPSs are usually defined from ordinary differential equations (ODEs) and reachability methods can be used to compute safe over-approximation of the solution set of ODEs. However, additional constraints, as obstacle avoidance have also to be considered to validate CPSs. To meet this need, we propose in this paper a framework, based on abstract domains, for solving constraint satisfaction problems where the objects manipulated are described by ODEs. We use a form of disjunctive completion for which we provide a split operator and an efficient constraint filtering mechanism that takes advantage of the continuity aspect of ODEs. We illustrate the benefits of our method on a real-world application of trajectory validation of a swarm of drones, for which the main property we aim to prove is the absence of collisions between drone trajectories. Our work has been concretized in the form of a cooperation between the DynIbex library, used for the abstraction of ODEs, and the AbSolute constraint solver, used for the constraint resolution. Experiments show promising results.

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Numeric Domains Meet Algebraic Data Types
Santiago Bautista, Thomas Jensen, and Benoît Montagu
(ENS Rennes, France; Inria, France)
We report on the design and formalization of a novel abstract domain, called numeric path relations (NPRs), that combines numeric relational domains with algebraic data types. This domain expresses relations between algebraic values that can contain scalar data. The construction of the domain is parameterized by the choice of a relational domain on scalar values. The construction employs projection paths on algebraic values, and in particular projections on variant cases, whose sound treatment is subtle due to mutual exclusiveness.

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Proving Array Properties using Data Abstraction
Julien Braine and Laure Gonnord
(University of Lyon, France; CNRS, France; Inria, France; LIP, France)
This paper presents a framework to abstract data structures within Horn clauses that allows abstractions to be easily expressed, compared, composed and implemented. These abstractions introduce new quantifiers that we eliminate with quantifier elimination techniques [].
We study the case of arrays and our experimental evaluation show promising results on classical array programs [].

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