Formal Analysis of Optical Systems

Khan-Afshar, Sanaz; Siddique, Umair; Mahmoud, Mohamed Yousri; Aravantinos, Vincent; Seddiki, Ons; Hasan, Osman; Tahar, Sofiène

doi:10.1007/s11786-014-0175-z

Cited by 14 publications

(10 citation statements)

References 60 publications

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“…Currently, fundamentals of ray optics, electromagnetic optics and quantum optics have been formalized [14] in HOL Light. This allowed the formal verification of some interesting and safety-critical optical systems such as optical resonators [19], laser resonator [13] and optical quantum flip gate [18].…”

Section: Formal Opticsmentioning

confidence: 99%

“…Physics is a heavy user of computation, and the pragmatic approach used sometimes by the HVG group is to just trust the results of computer algebra systems (e.g., using Mathematica to compute the numerical eigenvalues of the waveguide when there is no closed form solution [14]), temporarily adding them as axioms [14]. This is going to be a rich source of research problems for Calculemus-style projects, SMT solving, systems like MetiTarski, etc.…”

Section: Some Issues and Considerations In Formal Physicsmentioning

confidence: 99%

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Formalizing Physics: Automation, Presentation and Foundation Issues

Kaliszyk

Urban

Siddique

et al. 2015

Lecture Notes in Computer Science

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Abstract. In this paper, we report our first experiments in using learningassisted automated reasoning for the formal analysis of physical systems. In particular, we investigate the performance of automated proofs as compared to interactive ones done in HOL for the verification of ray and electromagnetic optics. Apart from automation, we also provide brief initial exploration of more general issues in formalization of physics, such as its presentation and foundations.

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Section: Formal Opticsmentioning

confidence: 99%

Section: Some Issues and Considerations In Formal Physicsmentioning

confidence: 99%

Formalizing Physics: Automation, Presentation and Foundation Issues

Kaliszyk

Urban

Siddique

et al. 2015

Lecture Notes in Computer Science

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“…ITP is also becoming an indispensable technology for verifying complex software-assisted proofs, and other complicated (e.g., hardware and software) designs. Other exact sciences, such as economics [39] and physics [2] have started to be fully formally encoded recently.…”

Section: Introduction: Formal Mathematics and Its Collaborative Aspectsmentioning

confidence: 99%

Wikis and Collaborative Systems for Large Formal Mathematics

Kaliszyk

Urban

2016

Semantic Web Collaborative Spaces

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In the recent years, there have been significant advances in formalization of mathematics, involving a number of large-scale formalization projects. This naturally poses a number of interesting problems concerning how should humans and machines collaborate on such deeply semantic and computer-assisted projects. In this paper we provide an overview of the wikis and web-based systems for such collaboration involving humans and also AI systems over the large corpora of fully formal mathematical knowledge.

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“…We also can refer to the work of Mahmoud et al 13,14 in quantum optics where formal verification of beam splitters and quantum flip gates are presented, respectively. To the best of our knowledge, the most comprehensive work on formalization of optical systems is a general framework presented in 2013, by Khan-Afshar et al, 15 to use theorem proving as a complement to computational and numerical approaches to improve analysis of optical system models, in ray, electromagnetic and quantum optics.…”

Section: Introductionmentioning

confidence: 99%

Formal analysis of electromagnetic optics

Khan-Afshar¹,

Hasan²,

Tahar³

2014

SPIE Proceedings

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Optical systems are increasingly being used in safety-critical applications. Due to the complexity and sensitivity of optical systems, their verification raises many challenges for engineers. Traditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide accurate results due to the risk of human error and inherent approximations of numerical algorithms. In order to overcome these limitations, we propose to use theorem proving (i.e., a computer-based technique that allows to express mathematical expressions and reason about their correctness by taking into account all the details of mathematical reasoning) as a complementary approach to improve optical system analysis. This paper provides a higher-order logic (a language used to express mathematical theories) formalization of electromagnetic optics in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our approach, we present the analysis of resonant cavity enhanced photonic devices.

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Formal Analysis of Optical Systems

Cited by 14 publications

References 60 publications

Formalizing Physics: Automation, Presentation and Foundation Issues

Formalizing Physics: Automation, Presentation and Foundation Issues

Wikis and Collaborative Systems for Large Formal Mathematics

Formal analysis of electromagnetic optics

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