A Verified Algorithm for Geometric Zonotope/Hyperplane Intersection

Immler, Fabian

doi:10.1145/2676724.2693164

Cited by 14 publications

(8 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This development does not handle division, which we do. Immler [21] has formalized AA in Isabelle/HOL; our own formalization shares a similar structure.…”

Section: Related Workmentioning

confidence: 99%

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

Becker

Zyuzin

Monat

et al. 2018

2018 Formal Methods in Computer Aided Design (FMCAD)

View full text Add to dashboard Cite

Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing. Due to the discrepancy between continuous reals and discrete finite-precision values, automated static analysis tools are highly valuable to estimate roundoff errors. The results, however, are only as correct as the implementations of the static analysis tools. This paper presents a formally verified and modular tool which fully automatically checks the correctness of finite-precision roundoff error bounds encoded in a certificate. We present implementations of certificate generation and checking for both Coq and HOL4 and evaluate it on a number of examples from the literature. The experiments use both in-logic evaluation of Coq and HOL4, and execution of extracted code outside of the logics: we benchmark Coq extracted unverified OCaml code and a CakeML-generated verified binary.

show abstract

“…This development does not handle division, which we do. Immler [21] has formalized AA in Isabelle/HOL; our own formalization shares a similar structure.…”

Section: Related Workmentioning

confidence: 99%

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

Becker

Zyuzin

Monat

et al. 2018

2018 Formal Methods in Computer Aided Design (FMCAD)

View full text Add to dashboard Cite

show abstract

“…The computation of convex hulls was also studied Meikle and Fleuriot, with the focus on using Hoare logic to support the reasoning framework [16] and by Immler in the case of zonotopes, with applications to the automatic proof of formulas [12].…”

Section: Related Workmentioning

confidence: 99%

Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs

Bertot

2018

Lecture Notes in Computer Science

View full text Add to dashboard Cite

This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex notions are those of boundary and separating edges. When performing proofs about this algorithm, questions of symmetry appear and this exposition attempts to give an account of how these symmetries can be handled. All this work relies on formal developments made with Coq and the mathematical components library. An Abstract Description of TriangulationGiven a set of points, a triangulating algorithm returns a collection of triangles that must cover the space between these points (the convex hull), have no overlap, and such that all the points of the input set are vertices of at least one triangle. When the input points represent obstacles, the triangulation can help construct safe routes between these obstacles, thanks to Delaunay triangulations and Voronoï diagrams.

show abstract

“…Frehse et al [30] cast the intersection operator as a convex minimization problem. Other research examines the problem of e ciently computing geometric intersections for particular choices of data structures [31,33,35,40].…”

Section: Related Workmentioning

confidence: 99%

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Bak

Bogomolov

Althoff

2017

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract.A promising technique for the formal verification of embedded and cyber-physical systems is flow-pipe construction, which creates a sequence of regions covering all reachable states over time. Flow-pipe construction methods can check whether specifications are met for all states, rather than just testing using a finite and incomplete set of simulation traces. A fundamental challenge when using flow-pipe construction on high-dimensional systems is the cost of geometric operations, such as intersection and convex hull. We address this challenge by showing that it is often possible to remove the need to perform high-dimensional geometric operations by combining two model transformations, direct time-triggered conversion and dynamics scaling. Further, we prove the overapproximation error in the conversion can be made arbitrarily small. Finally, we show that our transformation-based approach enables the analysis of a drivetrain system with up to 51 dimensions.

show abstract

A Verified Algorithm for Geometric Zonotope/Hyperplane Intersection

Cited by 14 publications

References 18 publications

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Contact Info

Product

Resources

About