Sofiène Tahar

Concordia University Montreal, Montréal, Quebec, Canada

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Publications (268)53.07 Total impact

  • O. Lahiouel · M.H. Zaki · S. Tahar ·
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    ABSTRACT: This paper presents an approach for enhancing analog circuit sizing using Satisfiability Modulo Theory (SMT). The circuit sizing problem is encoded using nonlinear constraints. An SMT-based algorithm exhaustively explores the design space, where the biasing-level design variables are conservatively tracked using a collection of hyperrectangles. The device dimensions are then determined by accurately relating biasing to geometry-level design parameters. We demonstrate the feasibility and efficiency of the proposed methodology on a two-stage amplifier and a folded cascode amplifier. Experimental results show that our approach can achieve higher quality in analog synthesis and unrivaled coverage of the design space.
  • Henda Aridhi · Mohamed H. Zaki · Sofiène Tahar ·
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    ABSTRACT: The reduction of the computational cost of statistical circuit analysis, such as Monte Carlo (MC) simulation, is a challenging problem. In this paper, we propose to build macromodels capable of reproducing the statistical behavior of all repeated MC simulations in a single simulation run. The parameter space is sampled similarly to the MC method and the resulting nonlinear models are reduced simultaneously to a small macromodel using nonlinear model order reduction method based on projection, perturbation theory and linearization techniques. We demonstrate the effectiveness of the proposed method for three applications: a current mirror, an operational transconductance amplifier, and a three inverter chain under the effect of current factor and threshold voltage variations. Our experimental results show that our method provides a speedup in the range 100–500 over 1000 samples of MC simulation.
    Analog Integrated Circuits and Signal Processing 07/2015; 85(3). DOI:10.1007/s10470-015-0588-x · 0.47 Impact Factor
  • U. Siddique · O. Hasan · S. Tahar ·
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    ABSTRACT: The prominent advantages of photonics are high bandwidth, low power and the possibility of better electromagnetic interference immunity. As a result, photonics technology is increasingly used in ubiquitous applications such as telecommunication, medicine, avionics and robotics. One of the main critical requirements is to verify the corresponding functional properties of these systems. In this perspective, we identify the most widely used modeling techniques (e.g., transfer matrices, difference equations and block diagrams) for the modeling and analysis of photonic components. Considering the safety and cost critical nature of the application domain, we discuss the potential of using formal methods as a complementary analysis approach. In particular, we propose a framework to formally specify and verify the critical properties of complex photonic systems within the sound core of a higher-order-logic theorem prover. For illustration purposes, we present the formal specification of a microring resonator based photonic filter along with the verification of some important design properties such as spectral power and filtering rejection ratio.
  • 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.
  • O. Hasan · W. Ahmed · S. Tahar · M.S. Hamdi ·
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    ABSTRACT: Reliability Block Diagrams (RBDs) allow us to model the failure relationships of complex systems and their sub-components and are extensively used for system reliability, availability, dependability and maintainability analyses of many engineering systems. Traditionally, Reliability Block Diagrams (RBD) are analyzed using paper-and-pencil proofs or computer simulations. Recently, formal techniques, including Petri Nets and higher-order-logic theorem proving, have been used for their analysis as well. In this paper, we provide a concise survey of these available RBD analysis techniques and compare them based on their accuracy, user friendliness and computational requirements.
    AIP Conference Proceedings 03/2015; 1648. DOI:10.1063/1.4913184
  • Hicham Chaoui · Navid Golbon · Imad Hmouz · Ridha Souissi · Sofiene Tahar ·
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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
  • U. Pervez · O. Hasan · K. Latif · S. Tahar · A. Gawanmeh · M.S. Hamdi ·
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    ABSTRACT: Fast Health Interoperable Resources (FHIR) is the recently proposed standard from HL7. Its distinguishing features include the user friendly implementation, support of built-in terminologies and for widely-used web standards. Given the safety-critical nature of FHIR, the rigorous analysis of e-health systems using the FHIR is a dire need since they are prone to failures. As a first step towards this direction, we propose to use probabilistic model checking, i.e., a formal probabilistic analysis approach, to assess the reliability of a typical e-health system used in hospitals based on the FHIR standard. In particular, we use the PRISM model checker to analyze the Markov Decision Process (MDP) and Continuous Time Markov Chain (CTMC) models to assess the failure probabilities of the overall system.
  • M.H. Zaki · S. Tahar · G. Al-Sammane · O. Hasan ·
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    ABSTRACT: This chapter proposes a complementary formal-based solution to the verification of analog and mixed-signal (AMS) designs. The authors use symbolic computation to model and verify AMS designs through the application of induction-based model checking. They also propose the use of higher order logic theorem proving to formally verify continuous models of analog circuits. To test and validate the proposed approaches, they developed prototype implementations in Mathematica and HOL and target analog and mixed-signal systems such as delta-sigma modulators.

  • Proc. of the 8th Conference on Intelligent Computer Mathematics (CICM'15); 01/2015
  • 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
  • O. Hasan · S. Tahar ·
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    ABSTRACT: Scientists and engineers often have to deal with systems that exhibit random or unpredictable elements and must effectively evaluate probabilities in each situation. Computer simulations, while the traditional tool used to solve such problems, are limited in the scale and complexity of the problems they can solve. Formalized Probability Theory and Applications Using Theorem Proving discusses some of the limitations inherent in computer systems when applied to problems of probabilistic analysis, and presents a novel solution to these limitations, combining higher-order logic with computer-based theorem proving. Combining practical application with theoretical discussion, this book is an important reference tool for mathematicians, scientists, engineers, and researchers in all STEM fields.
  • 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
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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.
  • 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.
  • Source
    Waqar Ahmed · Osman Hasan · Sofiene Tahar · Mohammad Salah Hamdi ·
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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.
  • Ibtissem Seghaier · Henda Aridhi · Mohamed H. Zaki · Sofiène Tahar ·
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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.
  • Source
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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.
  • Source
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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

Publication Stats

2k Citations
53.07 Total Impact Points


  • 1997-2015
    • Concordia University Montreal
      • Department of Electrical and Computer Engineering
      Montréal, Quebec, Canada
  • 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