On the Formalization of Z-Transform in HOL

Siddique, Umair; Mahmoud, Mohamed Yousri; Tahar, Sofiène

doi:10.1007/978-3-319-08970-6_31

Cited by 16 publications

(14 citation statements)

References 13 publications

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“…Our immediate future work is to explore the formal relation among the signalflow-graph representation and the Z-transform [21]. A potential utilization of our formalization and developed automation tactics is to build a framework to certify the results produced by informal tools such as MATLAB based SFG analysis program (available at [11]).…”

Section: Resultsmentioning

confidence: 99%

“…A more recent work about quantum formalization of coherent light has been reported in [15], with potential applications in the development of future quantum computers. Other interesting works are the formalization of Laplace transform [23] and Z-transform [21] in the HOL Light. Both of these transformations are less popular in the photonic community due to the additional overhead of transforming back-and-forth from time to frequency domain.…”

Section: Related Workmentioning

confidence: 99%

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On the Formal Analysis of Photonic Signal Processing Systems

Siddique¹,

Tahar²

2015

Formal Methods for Industrial Critical Systems

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Abstract. Photonic signal processing is an emerging area of research, which provides unique prospects to build high-speed communication systems. Recent advancements in fabrication technology allow on-chip manufacturing of signal processing devices. This fact has lead to the widespread use of photonics in industrial critical applications such as telecommunication, biophotonics and aerospace. One the most challenging aspects in the photonics industry is the accurate modeling and analysis of photonic devices due to the complex nature of light and optical components. In this paper, we propose to use higher-order-logic theorem proving to improve the analysis accuracy by overcoming the known limitations of incompleteness and soundness of existing approaches (e.g., paper-and-pencil based proofs and simulation). In particular, we formalize the notion of transfer function using the signal-flow-graph theory which is the most fundamental step to model photonic circuits. Consequently, we formalize and verify the important properties of the stability and the resonance of photonic systems. In order to demonstrate the effectiveness of the proposed infrastructure, we present the formal analysis of a widely used double-coupler double-ring (DCDR) photonic processor.

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Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

On the Formal Analysis of Photonic Signal Processing Systems

Siddique¹,

Tahar²

2015

Formal Methods for Industrial Critical Systems

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“…Such scenarios can compromise the safety of other vehicles on the highways and result in destabilizing the traffic flow [26]. Finally, it is interesting to consider two-dimensional platoons, which can be analyzed by combining our current framework and formalization of the z-Transform [27], which is already available in the HOL Light proof assistant.…”

Section: Discussionmentioning

confidence: 99%

Formal Verification of Platoon Control Strategies

Rashid

Siddique

Hasan

2018

Software Engineering and Formal Methods

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Recent developments in autonomous driving, vehicle-to-vehicle communication and smart traffic controllers have provided a hope to realize platoon formation of vehicles. The main benefits of vehicle platooning include improved safety, enhanced highway utility, efficient fuel consumption and reduced highway accidents. One of the central components of reliable and efficient platoon formation is the underlying control strategies, e.g., constant spacing, variable spacing and dynamic headway. In this paper, we provide a generic formalization of platoon control strategies in higher-order logic. In particular, we formally verify the stability constraints of various strategies using the libraries of multivariate calculus and Laplace transform within the sound core of HOL Light proof assistant. We also illustrate the use of verified stability theorems to develop runtime monitors for each controller, which can be used to automatically detect the violation of stability constraints in a runtime execution or a logged trace of the platoon controller. Our proposed formalization has two main advantages: 1) it provides a framework to combine both static (theorem proving) and dynamic (runtime) verification approaches for platoon controllers; and 2) it is inline with the industrial standards, which explicitly recommend the use of formal methods for functionalsafety, e.g., automotive ISO 26262.

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“…It sets a very strict standard but provides many automated tools and pre-verified mathematical theorems (for example, arithmetic, basic set theory, and real number analysis) to save user time. Siddique et al [18] used HOL Light to formalize Z transform and its region of convergence and a set of properties. As far as we know, the high-order theorem has not been applied to the verification of helicopter flight control systems.…”

Section: The Advantages and Disadvantages Of Coq Derivation And Compamentioning

confidence: 99%

Formal Verification of Helicopter Automatic Landing Control Algorithm in Theorem Prover Coq

Chen¹

2018

IJPE

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The helicopter flight control system plays an important role in helicopter flight and is known as the "brain" of the helicopter. Only when the system is verified correctly can the helicopter fly safely and steadily. This paper describes and validates the major part of an algorithm of automatic landing control in the high-order theorem prover Coq. Z transform is currently one of the most important flight control system analysis tools. This paper formally describes the definition of Z transform, validates some properties (i.e., homogeneous, uniformity, linear, and complex shift properties) of Z transform to extend the system analysis capabilities of theorem proving, and lays the foundation for further formalization of the helicopter flight control system.

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On the Formalization of Z-Transform in HOL

Cited by 16 publications

References 13 publications

On the Formal Analysis of Photonic Signal Processing Systems

On the Formal Analysis of Photonic Signal Processing Systems

Formal Verification of Platoon Control Strategies

Formal Verification of Helicopter Automatic Landing Control Algorithm in Theorem Prover Coq

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