Sofiène Tahar

Concordia University Montreal, Montréal, Quebec, Canada

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Publications (253)32.67 Total impact

  • 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: 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.
    05/2014;
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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.
    05/2014;
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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.
    05/2014;
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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.
    05/2014;
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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.
    05/2014;
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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).
  • 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. · 1.00 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: 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.
    Proc SPIE 09/2013;
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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;
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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;
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    Naeem Abbasi, Osman Hasan, Sofiène Tahar
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    ABSTRACT: Modeling and analysis of soft errors in electronic circuits has traditionally been done using computer simulations. Computer simulations cannot guarantee correctness of analysis because they utilize approximate real number representations and pseudo random numbers in the analysis and thus are not well suited for analyzing safety-critical applications. In this paper, we present a higher-order logic theorem proving based method for modeling and analysis of soft errors in electronic circuits. Our developed infrastructure includes formalized continuous random variable pairs, their Cumulative Distribution Function (CDF) properties and independent standard uniform and Gaussian random variables. We illustrate the usefulness of our approach by modeling and analyzing soft errors in commonly used dynamic random access memory sense amplifier circuits.
    07/2013;
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    ABSTRACT: Classified Markov chains have been extensively applied to model and analyze various stochastic systems in many engineering and scientific domains. Traditionally, the analysis of these systems has been conducted using computer simulations and, more recently, also probabilistic model-checking. However, these methods either cannot guarantee accurate analysis or are not scalable due to the unacceptable computation times. As an alternative approach, this paper proposes to reason about classified Markov chains using HOL theorem proving. We provide a formalization of classified discrete-time Markov chains with finite state space in higher-order logic and the formal verification of some of their widely used properties. To illustrate the usefulness of the proposed approach, we present the formal analysis of a generic LRU (least recently used) stack model.
    Proceedings of the 4th international conference on Interactive Theorem Proving; 07/2013
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    ABSTRACT: The performance of Wireless Sensor Networks (WSNs) is traditionally analyzed using simulation or paper-and-pencil proof methods. However, such methods cannot ascertain accurate analysis, which is a serious drawback for safety and financial-critical applications. In order to overcome this limitation, we propose to use a higher-order-logic theorem prover (HOL) to formally analyze the performance of WSNs. In particular, this paper presents a generic formal performance analysis methodology for WSNs using the k-set randomized scheduling as an energy saving approach. The proposed methodology is primarily based on the formalized theories of measure and probability. For illustration purposes, we formally analyze the performance of a WSN deployed for volcanic earthquake detection.
    Workshops on Enabling Technologies: Infrastracture for Collaborative Enterprises (WETICE), Hammamet, Tunisia; 06/2013
  • Tarek Mhamdi, Osman Hasan, Sofiène Tahar
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    ABSTRACT: Dynamic systems that exhibit probabilistic behavior represent a large class of man-made systems such as communication networks, air traffic control, and other mission-critical systems. Evaluation of quantitative issues like performance and dependability of these systems is of paramount importance. In this paper, we propose a generalized methodology to formally reason about probabilistic systems within a theorem prover. We present a formalization of measure theory in the HOL theorem prover and use it to formalize basic concepts from the theory of probability. We also use the Lebesgue integration to formalize statistical properties of random variables. To illustrate the practical effectiveness of our methodology, we formally prove classical results from the theories of probability and information and use them in a data compression application in HOL.
    ACM Transactions on Embedded Computing Systems (TECS). 01/2013; 12(1).
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    ABSTRACT: In this work we provide a methodology for the design and verification of a frequency domain equalizer. The performance analysis of the equalizer is conducted using two methods: simulation based verification in Simulink and System Generator and theorem proving techniques in Higher Order Logic. We conduct both floating-point and fixed-point error estimations for the design in Simulink and System Generator, respectively. Then, we use formal error analysis based on the theorem proving to verify an implementation of the frequency domain equalizer based on the Fast LMS algorithm. The formal error analysis and simulation based error estimation of the algorithm intend to show that, when converting from one number domain to another, the algorithm produces the same values with an accepted error margin caused by the round-off error accumulation. This work shows the efficiency of combining simulation and formal verification based methods in verifying complex systems such as the frequency domain equalizer.
    Microelectronics Journal 01/2013; · 0.91 Impact Factor
  • NASA Formal Methods, Edited by Brat, Guillaume and Rungta, Neha and Venet, Arnaud, 01/2013: pages 368-382; Springer Berlin Heidelberg., ISBN: 9783642380877
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    ABSTRACT: Geometrical optics, in which light is characterized as rays, provides an efficient and scalable formalism for the modeling and analysis of optical and laser systems. The main applications of geometrical optics are in stability analysis of optical resonators, laser mode locking and micro opto-electro-mechanical systems. Traditionally, the analysis of such applications has been carried out by informal techniques like paper-and-pencil proof methods, simulation and computer algebra systems. These traditional techniques cannot provide accurate results and thus cannot be recommended for safety-critical applications, such as corneal surgery, process industry and inertial confinement fusion. On the other hand, higher-order logic theorem proving does not exhibit the above limitations, thus we propose a higher-order logic formalization of geometrical optics. Our formalization is mainly based on existing theories of multivariate analysis in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our formalization, we present the modeling and stability analysis of some optical resonators in HOL Light.
    Automated Deduction in Geometry, Edited by Ida, Tetsuo and Fleuriot, Jacques, 01/2013: pages 161-180; Springer Berlin Heidelberg., ISBN: 9783642406713
  • Liya Liu, Osman Hasan, Sofiène Tahar
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    ABSTRACT: Markov chains are extensively used in modeling different aspects of engineering and scientific systems, such as performance of algorithms and reliability of systems. Different techniques have been developed for analyzing Markovian models, for example, Markov Chain Monte Carlo based simulation, Markov Analyzer, and more recently probabilistic model-checking. However, these techniques either do not guarantee accurate analysis or are not scalable. Higher-order-logic theorem proving is a formal method that has the ability to overcome the above mentioned limitations. However, it is not mature enough to handle all sorts of Markovian models. In this paper, we propose a formalization of Discrete-Time Markov Chain (DTMC) that facilitates formal reasoning about time-homogeneous finite-state discrete-time Markov chain. In particular, we provide a formal verification on some of its important properties, such as joint probabilities, Chapman-Kolmogorov equation, reversibility property, using higher-order logic. To demonstrate the usefulness of our work, we analyze two applications: a simplified binary communication channel and the Automatic Mail Quality Measurement protocol.
    Journal of Computer Science and Technology 01/2013; 28(2). · 0.48 Impact Factor

Publication Stats

1k Citations
32.67 Total Impact Points

Institutions

  • 1997–2014
    • 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
  • 2006
    • West Virginia University
      • Department of Computer Science & Electrical Engineering
      Morgantown, WV, United States
    • Queen Mary, University of London
      Londinium, England, United Kingdom
  • 2001
    • Middlesex University, UK
      • Department of Computer Science
      London, ENG, United Kingdom