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Formal verification of an interior point algorithm instanciation
With the increasing power of computers, real-time algorithms tends to be...
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Formal Verification of End-to-End Learning in Cyber-Physical Systems: Progress and Challenges
Autonomous systems – such as self-driving cars, autonomous drones, and a...
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Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs
This extended abstract is about an effort to build a formal description ...
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Convex Hull Calculations: a Matlab Implementation and Correctness Proofs for the lrs-Algorithm
This paper provides full -code and informal correctness proofs for the l...
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Towards Deriving Verification Properties
Formal software verification uses mathematical techniques to establish t...
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Formal Analysis of Non-functional Properties for a Cooperative Automotive System
Modeling and analysis of nonfunctional requirements is crucial in automo...
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Understanding the QuickXPlain Algorithm: Simple Explanation and Formal Proof
In his seminal paper of 2004, Ulrich Junker proposed the QuickXPlain alg...
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Verification and Validation of Convex Optimization Algorithms for Model Predictive Control
Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably stronger design constraints that arise when the applications of interest, such as aerospace systems, are safety-critical. Formal verification is the process of proving or disproving the ”correctness” of an algorithm with respect to a certain mathematical description of it by means of a computer. This article discusses the formal verification of the Ellipsoid method, a convex optimization algorithm, and its code implementation as it applies to receding horizon control. Options for encoding code properties and their proofs are detailed. The applicability and limitations of those code properties and proofs are presented as well. Finally, floating-point errors are taken into account in a numerical analysis of the Ellipsoid algorithm. Modifications to the algorithm are presented which can be used to control its numerical stability.
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