Verification of Numerical Programs: From Real Numbers to Floating Point Numbers

Goodloe, Alwyn E.; Muñoz, César; Kirchner, Florent; Correnson, Loiec

doi:10.1007/978-3-642-38088-4_31

Cited by 29 publications

(21 citation statements)

References 3 publications

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“…Unfortunately, the finitary nature of floating-point, along with its uneven distribution of representable numbers introduces round-off errors, as well as does not preserve many familiar laws (e.g., associativity of +) [22]. This mismatch often necessitates re-verification using tools that precisely compute round-off error bounds (e.g., as illustrated in [21]). While SMT solvers can be used for small problems [52,24], the need to scale necessitates the use of various abstract interpretation methods [11], the most popular choices being interval [41] or affine arithmetic [54].…”

Section: Introductionmentioning

confidence: 99%

Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions

Solovyev

Jacobsen

Rakamarić

et al. 2015

FM 2015: Formal Methods

123

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Rigorous estimation of maximum floating-point round-off errors is an important capability central to many formal verification tools. Unfortunately, available techniques for this task often provide overestimates. Also, there are no available rigorous approaches that handle transcendental functions. We have developed a new approach called Symbolic Taylor Expansions that avoids this difficulty, and implemented a new tool called FPTaylor embodying this approach. Key to our approach is the use of rigorous global optimization, instead of the more familiar interval arithmetic, affine arithmetic, and/or SMT solvers. In addition to providing far tighter upper bounds of round-off error in a vast majority of cases, FPTaylor also emits analysis certificates in the form of HOL Light proofs. We release FPTaylor along with our benchmarks for evaluation. Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor ExpansionsAlexey Solovyev, Charles Jacobsen, Zvonimir Rakamarić, and Ganesh Gopalakrishnan School of Computing, University of Utah, Salt Lake City, UT 84112, USA {monad,charlesj,zvonimir,ganesh}@cs.utah.edu Abstract. Rigorous estimation of maximum floating-point round-off errors is an important capability central to many formal verification tools. Unfortunately, available techniques for this task often provide overestimates. Also, there are no available rigorous approaches that handle transcendental functions. We have developed a new approach called Symbolic Taylor Expansions that avoids this difficulty, and implemented a new tool called FPTaylor embodying this approach. Key to our approach is the use of rigorous global optimization, instead of the more familiar interval arithmetic, affine arithmetic, and/or SMT solvers. In addition to providing far tighter upper bounds of round-off error in a vast majority of cases, FPTaylor also emits analysis certificates in the form of HOL Light proofs. We release FPTaylor along with our benchmarks for evaluation.

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Section: Introductionmentioning

confidence: 99%

Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions

Solovyev

Jacobsen

Rakamarić

et al. 2015

FM 2015: Formal Methods

123

View full text Add to dashboard Cite

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“…Although Goodloe et al [8] formally verify programs for aerospace applications, namely airborne conflict detection and resolution (CD&R), their approach is in general very similar to ours. Their objective is to verify whether a checker correctly determines that two aircraft maintain a minimum separation distance.…”

Section: Data Analysis Of the Safe Distance Problemmentioning

confidence: 88%

“…Hence, when comparing our work with others, those parameters are set to zero. In general, all related works discussed here except the work by Goodloe et al [8] are incomplete, and those in the domain of transportation engineering (discussed here) are not formally proved.…”

Section: Data Analysis Of the Safe Distance Problemmentioning

confidence: 91%

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A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles

Rizaldi

Immler

Althoff

2016

Lecture Notes in Computer Science

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Abstract. One barrier in introducing autonomous vehicle technology is the liability issue when these vehicles are involved in an accident. To overcome this, autonomous vehicle manufacturers should ensure that their vehicles always comply with traffic rules. This paper focusses on the safe distance traffic rule from the Vienna Convention on Road Traffic. Ensuring autonomous vehicles to comply with this safe distance rule is problematic because the Vienna Convention does not clearly define how large a safe distance is. We provide a formally proved prescriptive definition of how large this safe distance must be, and correct checkers for the compliance of this traffic rule. The prescriptive definition is obtained by: 1) identifying all possible relative positions of stopping (braking) distances; 2) selecting those positions from which a collision freedom can be deduced; and 3) reformulating these relative positions such that lower bounds of the safe distance can be obtained. These lower bounds are then the prescriptive definition of the safe distance, and we combine them into a checker which we prove to be sound and complete. Not only does our work serve as a specification for autonomous vehicle manufacturers, but it could also be used to determine who is liable in court cases and for online verification of autonomous vehicles' trajectory planner.

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“…Finally, some preliminary experiments have been done to use WP for verifying accuracy of floating point computations. This work follows the methodology devised in an earlier collaboration with NASA (Goodloe, Muñoz, Kirchner, & Correnson, 2013).…”

Section: Unitary Analysismentioning

confidence: 99%

Defining a pragmatic methodology for software assessment based on a "white-box" approach

Duboc¹,

Sadmi²,

Kirchner³

2016

Congrès Lambda Mu 20 De Maîtrise Des Risques Et De Sûreté De Fonctionnement

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SummaryThe present paper sums up the work and results of an on-going partnership program between BUREAU VERITAS & the CEA LIST, started in 2015, whose main objective is to propose a generic and pragmatic methodology in the form of a set of guidelines for software development and assessment. Initiated by the observation of an absence of dedicated software safety assessment standards and tools in several industrial sectors, and benefiting from the BUREAU VERITAS knowledge of software safety certification standards and the CEA LIST expertise in software code verification, these guidelines are focusing on development processes and the use of efficient tools to verify software through a white-box approach. They have been designed to be usable in all the domains that deal with the quality, reliability and/or safety of software systems, especially in sectors where safety concerns are not prevalent (e.g. car amenities -multimedia, air conditioning, etc.-, robotics and smart devices -automated handling, connected bracelets and watches, etc.-) or those lacking existing regulations (e.g. marine & offshore, part of the defense sector, industrial and agricultural machines, etc.). RésuméCet article récapitule le travail et les résultats d'un programme de partenariat entre BUREAU VERITAS & le CEA LIST, initié en 2015, dont l'objectif principal est la proposition d'une méthodologie générique et pragmatique sous la forme d'une liste de recommandations pour le développement et l'évaluation de logiciels. Partant du constat qu'un certain nombre de secteurs industriels ne bénéficient pas de référentiel dédié ni d'outils associés pour l'évaluation de la sécurité du logiciel, et profitant de la connaissance par BUREAU VERITAS des référentiels de certification de la sécurité du logiciel et de l'expertise du CEA LIST en vérification de code logiciel, ces recommandations se concentrent sur les processus de développement et l'utilisation d'outils efficaces pour vérifier le logiciel par une approche « boîte-blanche ». Elles ont été élaborées pour être applicables dans tout domaine s'appuyant sur la qualité, la fiabilité et/ou la sécurité des logiciels, notamment dans les secteurs où les préoccupations liées à la sécurité sont moins prégnantes (ex. des équipements automobiles -multimédia, air conditionné, etc.-, la robotique et les appareils intelligents -systèmes de manutention automatisés, montres et bracelets connectés, etc.) ou ceux qui ne possèdent pas de réglementations existantes (ex. la marine & offshore, une partie du secteur de la défense, les machines industrielles et agricoles, etc.).

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Verification of Numerical Programs: From Real Numbers to Floating Point Numbers

Cited by 29 publications

References 3 publications

Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions

Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions

A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles

Defining a pragmatic methodology for software assessment based on a "white-box" approach

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