Sofiène Tahar

Concordia University Montreal, Montréal, Quebec, Canada

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Publications (260)50.43 Total impact

  • Umair Siddique · Osman Hasan · Sofiène Tahar
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    ABSTRACT: Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.
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    ABSTRACT: This paper presents an adaptive state of charge (SOC) and state of health (SOH) estimation technique for lithium-ion batteries. The adaptive strategy estimates online parameters of the battery model using a Lyapunov-based adaptation law. Therefore, the adaptive observer stability is guaranteed by Lyapunov's direct method. Since no a priori knowledge of battery parameters is required, accurate estimation is still achieved, although parameters change due to aging or other factors. Unlike other estimation strategies, only battery terminal voltage and current measurements are required. Simulation and experimental results highlight the high SOC and SOH accuracy estimation of the proposed technique.
    IEEE Transactions on Industrial Electronics 03/2015; 62(3):1610-1618. DOI:10.1109/TIE.2014.2341576 · 6.50 Impact Factor
  • Henda Aridhi · Mohamed H. Zaki · Sofiene Tahar
    IEEE Transactions on Very Large Scale Integration (VLSI) Systems 01/2015; DOI:10.1109/TVLSI.2015.2421450 · 1.36 Impact Factor
  • Vincent Aravantinos · Sofiene Tahar
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    ABSTRACT: Reducing the distance between informal and formal proofs in interactive theorem proving is a long-standing matter. An approach to this general topic is to increase automation in theorem provers: indeed, automation turns many small formal steps into one big step. In spite of the usual automation methods, there are still many situations where the user has to provide some information manually, whereas this information could be derived from the context. In this paper, we characterize some very common use cases where such situations happen, and identify some general patterns behind them. We then provide solutions to deal with these situations automatically, which we implemented as HOL Light and HOL4 tactics. We find these tactics to be extremely useful in practice, both for their automation and for the feedback they provide to the user.
    ITP 2014, Vienna, Austria; 08/2014
  • Umair Siddique · Mohamed Yousri Mahmoud · Sofiène Tahar
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    ABSTRACT: System analysis based on difference or recurrence equations is the most fundamental technique to analyze biological, electronic, control and signal processing systems. Z-transform is one of the most popular tool to solve such difference equations. In this paper, we present the formalization of Z-transform to extend the formal linear system analysis capabilities using theorem proving. In particular, we use differential, transcendental and topological theories of multivariate calculus to formally define Z-transform in higher-order logic and reason about the correctness of its properties, such as linearity, time shifting and scaling in z-domain. To illustrate the practical effectiveness of the proposed formalization, we present the formal analysis of an infinite impulse response (IIR) digital signal processing filter.
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    ABSTRACT: It is customary to assess the reliability of underground oil and gas pipelines in the presence of excessive loading and corrosion effects to ensure a leak-free transport of hazardous materials. The main idea behind this reliability analysis is to model the given pipeline system as a Reliability Block Diagram (RBD) of segments such that the reliability of an individual pipeline segment can be represented by a random variable. Traditionally, computer simulation is used to perform this reliability analysis but it provides approximate results and requires an enormous amount of CPU time for attaining reasonable estimates. Due to its approximate nature, simulation is not very suitable for analyzing safety-critical systems like oil and gas pipelines, where even minor analysis flaws may result in catastrophic consequences. As an accurate alternative, we propose to use a higher-order-logic theorem prover (HOL) for the reliability analysis of pipelines. As a first step towards this idea, this paper provides a higher-order-logic formalization of reliability and the series RBD using the HOL theorem prover. For illustration, we present the formal analysis of a simple pipeline that can be modeled as a series RBD of segments with exponentially distributed failure times.
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    ABSTRACT: Simulation cannot give a full coverage of Phase Locked Loop (PLL) behavior in presence of process variation, jitter and varying initial conditions. Qualitative Simulation is an attracting method that computes behavior envelopes for dynamical systems over continuous ranges of their parameters. Therefore, this method can be employed to verify PLLs locking property given a model that encompasses their imperfections. Extended System of Recurrence Equations (ESREs) offer a unified modeling language to model analog and digital PLLs components. In this paper, an ESRE model is created for both PLLs and their imperfections. Then, a modified qualitative simulation algorithm is used to guarantee that the PLL locking time is sound for every possible initial condition and parameter value. We used our approach to analyze a Charge Pump-PLL for a $0.18\mu m$ fabrication process and in the presence of jitter and initial conditions uncertainties. The obtained results show an improvement of simulation coverage by computing the minimum locking time and predicting a non locking case that statistical simulation technique fails to detect.
  • Paul Winkler · Henda Aridhi · Mohamed H. Zaki · Sofiene Tahar
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    ABSTRACT: The generation of fast models for device level circuit descriptions is a very active area of research. Model order reduction is an attractive technique for dynamical models size reduction. In this paper, we propose an approach based on clustering, curve-fitting, linearization and Krylov space projection to build reduced models for nonlinear analog circuits. We demonstrate our model order reduction method for three nonlinear circuits: a voltage controlled oscillator, an operational amplifier and a digital frequency divider. Our experimental results show that the reduced models lead to an improvement in simulation speed while guaranteeing the representation of the behavior of the original circuit design.
  • Ons Lahiouel · Henda Aridhi · Mohamed H. Zaki · Sofiene Tahar
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    ABSTRACT: We propose an environment for the verification of analog circuits behavioral properties, where the circuit state space bounds are first computed using qualitative simulation. Then, their specified behavioral properties are verified on these bounds. The effectiveness of the method is illustrated with a tunnel diode oscillator.
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    ABSTRACT: Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting this analysis within the sound core of a theorem prover: HOL Light. Our definition of complex vector builds upon the definitions of complex numbers and real vectors. This extension allows us to extensively benefit from the already verified theorems based on complex analysis and real vector analysis. To show the practical usefulness of our library we adopt it to formalize electromagnetic fields and to prove the law of reflection for the planar waves.
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    ABSTRACT: Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical system models using traditional paper-and-pencil and computer simulation approaches sets limits especially in safety-critical applications. In order to overcome these limitations, we propose to employ higher-order-logic theorem proving as a complement to computational and numerical approaches to improve optical model analysis in a comprehensive framework. The proposed framework allows formal analysis of optical systems at four abstraction levels, i.e., ray, wave, electromagnetic, and quantum.
    Mathematics in Computer Science 03/2014; 8(1). DOI:10.1007/s11786-014-0175-z
  • Naeem Abbasi · Osman Hasan · Sofiène Tahar
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    ABSTRACT: Recently proposed formal reliability analysis techniques have overcome the inaccuracies of traditional simulation based techniques but can only handle problems involving discrete random variables. In this paper, we extend the capabilities of existing theorem proving based reliability analysis by formalizing several important statistical properties of continuous random variables like the second moment and the variance. We also formalize commonly used concepts about the reliability theory such as survival, hazard, cumulative hazard and fractile functions. With these extensions, it is now possible to formally reason about important measures of reliability (the probabilities of failure, the failure risks and the mean-time-to failure) associated with the life of a system that operates in an uncertain and harsh environment and is usually continuous in nature. We illustrate the modeling and verification process with the help of examples involving the reliability analysis of essential electronic and electrical system components.
    Journal of Computer and System Sciences 03/2014; 80(2):323–345. DOI:10.1016/j.jcss.2013.05.002 · 1.14 Impact Factor
  • Umair Siddique · Sofiène Tahar
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    ABSTRACT: Recently, optics technology has emerged as a promising solution by resolving critical bottlenecks in conventional electronic systems. Its application domain spans over diverse fields ranging from laser surgeries to space telescopes. In this paper, we describe an ongoing project which aims at building a theorem proving based framework for the formal reasoning about geometrical optics, an essential theory required in the design and analysis of optical systems. Mainly, we present the motivation of our work, a road-map to achieve our goals, current status of the project and future milestones.
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    ABSTRACT: Quantum computers are promising to efficiently solve hard computational problems, especially NP problems. In this paper, we propose to tackle the formal verification of quantum circuits using theorem proving. In particular, we focus on the verification of quantum computing based on coherent light, which is typically light produced by laser sources. We formally verify the behavior of the quantum flip gate in HOL Light: we prove that it can flip a zero-quantum-bit to a one-quantum-bit and vice versa. To this aim, we model two optical devices: the beam splitter and the phase conjugating mirror and prove relevant properties about them. Then by cascading the two elements and utilizing these properties, the complete model of the flip gate is formally verified. This requires the formalization of some fundamental mathematics like exponentiation of linear transformations.
  • Maissa Elleuch · Osman Hasan · Sofiène Tahar · Mohamed Abid
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    ABSTRACT: In the context of wireless sensor networks (WSNs), the ability to detect an intrusion event is the most desired characteristic. Due to the randomness in nodes scheduling algorithm and sensor deployment, probabilistic techniques are used to analyze the detection properties of WSNs. However traditional probabilistic analysis techniques, such as simulation and model checking, do not ensure accurate results, which is a severe limitation considering the mission-critical nature of most of the WSNs. In this paper, we overcome these limitations by using higher-order-logic theorem proving to formally analyze the detection properties of randomly-deployed WSNs using the randomized scheduling of nodes. Based on the probability theory, available in the HOL theorem prover, we first formally reason about the intrusion period of any occurring event. This characteristic is then built upon to develop the fundamental formalizations of the key detection metrics: the detection probability and the detection delay. For illustration purposes, we formally analyze the detection performance of a WSN deployed for border security monitoring.
    Formal Aspects of Computing 01/2014; 27(1):79-102. DOI:10.1007/s00165-014-0304-0 · 0.81 Impact Factor
  • Umair Siddique · Sofiene Tahar
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    ABSTRACT: Recent developments in the fabrication technology attracted the attention of optical engineers and physicists in the area of VLSI photonics. Due to the physical nature of light-wave systems and their usage in safety critical domains such as human surgeries and high budget space missions, it is indispensable to build high assurance systems. Traditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide perfectly 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 higher-order logic theorem proving to improve the analysis in the domain of integrated optics or VLSI photonics. In particular, this paper provides a higher-order logic formalization of optical microresonators which are the most fundamental building blocks of many photonic devices. In order to illustrate the practical utilization of our work, we present the formal analysis of 2-D microresonator lattice optical filters.
    Design Automation and Test in Europe; 01/2014
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    ABSTRACT: Noise and process variation present a practical limit on the performance of analog circuits. This paper proposes a methodology for modeling and verification of analog designs in the presence of shot noise, thermal noise, and process variations. The idea is to use stochastic differential equations to model noise in additive and multiplicative form and then combine process variation due to 0.18 μm technology in a statistical run-time verification environment. The efficiency of Monte-Carlo and Bootstrap statistical techniques are compared for a Colpitts oscillator and a phase locked loop-based frequency synthesizer circuit.
    IEEE Transactions on Very Large Scale Integration (VLSI) Systems 10/2013; 21(10):1811-1822. DOI:10.1109/TVLSI.2012.2219083 · 1.36 Impact Factor
  • Umair Siddique · Vincent Aravantinos · Sofiène Tahar
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    ABSTRACT: Optical systems are increasingly used in microsystems, telecommunication, aerospace and laser industry. Due to the complexity and sensitivity of optical systems, their verification poses many challenges to 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 perfectly 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 them by taking into account all the details of mathematical reasoning) as an alternative to computational and numerical approaches to improve optical system analysis in a comprehensive framework. In particular, this paper provides a higher-order logic (a language used to express mathematical theories) formalization of ray optics in the HOL Light theorem prover. Based on the multivariate analysis library of HOL Light, we formalize the notion of light ray and optical system (by defining medium interfaces, mirrors, lenses, etc.), i.e., we express these notions mathematically in the software. This allows us to derive general theorems about the behavior of light in such optical systems. In order to demonstrate the practical effectiveness, we present the stability analysis of a Fabry-Perot resonator.
    Proceedings of SPIE - The International Society for Optical Engineering 09/2013; 8844. DOI:10.1117/12.2024860 · 0.20 Impact Factor
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    ABSTRACT: In top-down multi-level design methodologies, design descriptions at higher levels of abstraction are incrementally refined to the final realizations. Simulation based techniques have traditionally been used to verify that such model refinements do not change the design functionality. Unfortunately, with computer simulations it is not possible to completely check that a design transformation is correct in a reasonable amount of time, as the number of test patterns required to do so increase exponentially with the number of system state variables. In this paper, we propose a methodology for the verification of conformance of models generated at higher levels of abstraction in the design process to the design specifications. We model the system behavior using sequence of recurrence equations. We then use symbolic simulation together with equivalence checking and property checking techniques for design verification. Using our proposed method, we have verified the equivalence of three WiMax system models at different levels of design abstraction, and the correctness of various system properties on those models. Our symbolic modeling and verification experiments show that the proposed verification methodology provides performance advantage over its numerical counterpart.
    07/2013; 122. DOI:10.4204/EPTCS.122.3
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    Maissa Elleuch · Osman Hasan · Sofiène Tahar · Mohamed Abid
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    ABSTRACT: Wireless Sensor Networks (WSNs) have been widely explored for forest fire detection, which is considered a fatal threat throughout the world. Energy conservation of sensor nodes is one of the biggest challenges in this context and random scheduling is frequently applied to overcome that. The performance analysis of these random scheduling approaches is traditionally done by paper-and-pencil proof methods or simulation. These traditional techniques cannot ascertain 100% accuracy, and thus are not suitable for analyzing a safety-critical application like forest fire detection using WSNs. In this paper, we propose to overcome this limitation by applying formal probabilistic analysis using theorem proving to verify scheduling performance of a real-world WSN for forest fire detection using a k-set randomized algorithm as an energy saving mechanism. In particular, we formally verify the expected values of coverage intensity, the upper bound on the total number of disjoint subsets, for a given coverage intensity, and the lower bound on the total number of nodes.
    07/2013; 122. DOI:10.4204/EPTCS.122.1

Publication Stats

2k Citations
50.43 Total Impact Points


  • 1997–2015
    • Concordia University Montreal
      • Department of Electrical and Computer Engineering
      Montréal, Quebec, Canada
  • 2010
    • National University of Science and Technology
      • School of Electrical Engineering and Computer Science
      Islāmābād, Islamabad Capital Territory, Pakistan
  • 2008–2009
    • The German University in Cairo
      Al Qāhirah, Al Qāhirah, Egypt
    • Nanyang Technological University
      • School of Electrical and Electronic Engineering
      Singapore, Singapore
  • 1996–2007
    • Université de Montréal
      • Department of Computer Science and Operations Research
      Montréal, Quebec, Canada
  • 2001
    • Middlesex University, UK
      • Department of Computer Science
      London, ENG, United Kingdom