Prime Implicants

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Samuele Baronchelli - One of the best experts on this subject based on the ideXlab platform.

  • A COMPUTATIONAL FRAMEWORK FOR Prime Implicants IDENTIFICATION IN NON-COHERENT DYNAMIC SYSTEMS
    2016
    Co-Authors: Francesco Di Maio, Samuele Baronchelli, Enrico Zio
    Abstract:

    Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., Event Trees (ETs) and Fault Trees (FTs)) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this paper, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the Prime Implicants (PIs) of the dynamic system. The framework entails adopting a Multiple-Valued Logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a Differential Evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic non-coherent system composed by five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases.

  • A Visual Interactive Method for Prime Implicants Identification
    IEEE Transactions on Reliability, 2015
    Co-Authors: Francesco Di Maio, Samuele Baronchelli, Enrico Zio
    Abstract:

    We propose a visual interactive method for the identification of the Prime Implicants (PIs) of dynamic non-coherent systems. Visual interactive methods integrate mathematical and symbolic models with runtime interaction and real-time graphic display, which allow visualizing the underlying physical relationships among process parameters. The proposed method is based on a parallel coordinates data mining tool that relies on an innovative pruning procedure which, on the basis of a proper selection of characteristic features of the accident sequences, retrieves the PIs among the whole set of Implicants in terms of process parameters values and/or components failure states. The method is exemplified on an artificial case study and, then, applied for the dynamic reliability analysis of the Airlock System (AS) of a CANDU reactor.

  • A Visual Interactive Method for Prime Implicants Identification
    IEEE Transactions on Reliability, 2015
    Co-Authors: Francesco Di Maio, Samuele Baronchelli
    Abstract:

    We propose a visual interactive method for the identification of the Prime Implicants (PIs) of dynamic non-coherent systems. Visual interactive methods integrate mathematical and symbolic models with runtime interaction and real-time graphic display, which allow visualizing the underlying physical relationships among process parameters. The proposed method is based on a parallel coordinates data mining tool that relies on an innovative pruning procedure which, on the basis of a proper selection of characteristic features of the accident sequences, retrieves the PIs among the whole set of Implicants in terms of process parameter values or component failure states or both. The method is exemplified on an artificial case study, and then applied to the dynamic reliability analysis of the Airlock System of a Canadian Deuterium Uranium reactor.

  • A Computational Framework for Prime Implicants Identification in Noncoherent Dynamic Systems
    Risk Analysis, 2014
    Co-Authors: Francesco Di Maio, Samuele Baronchelli
    Abstract:

    Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., event trees [ETs] and fault trees [FTs]) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time†dependent model that includes the dependencies with the stochastic transition events. In this article, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the Prime Implicants (PIs) of the dynamic system. The framework entails adopting a multiple†valued logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a differential evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic noncoherent system composed of five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases.

Francesco Di Maio - One of the best experts on this subject based on the ideXlab platform.

  • A COMPUTATIONAL FRAMEWORK FOR Prime Implicants IDENTIFICATION IN NON-COHERENT DYNAMIC SYSTEMS
    2016
    Co-Authors: Francesco Di Maio, Samuele Baronchelli, Enrico Zio
    Abstract:

    Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., Event Trees (ETs) and Fault Trees (FTs)) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this paper, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the Prime Implicants (PIs) of the dynamic system. The framework entails adopting a Multiple-Valued Logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a Differential Evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic non-coherent system composed by five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases.

  • A Visual Interactive Method for Prime Implicants Identification
    IEEE Transactions on Reliability, 2015
    Co-Authors: Francesco Di Maio, Samuele Baronchelli, Enrico Zio
    Abstract:

    We propose a visual interactive method for the identification of the Prime Implicants (PIs) of dynamic non-coherent systems. Visual interactive methods integrate mathematical and symbolic models with runtime interaction and real-time graphic display, which allow visualizing the underlying physical relationships among process parameters. The proposed method is based on a parallel coordinates data mining tool that relies on an innovative pruning procedure which, on the basis of a proper selection of characteristic features of the accident sequences, retrieves the PIs among the whole set of Implicants in terms of process parameters values and/or components failure states. The method is exemplified on an artificial case study and, then, applied for the dynamic reliability analysis of the Airlock System (AS) of a CANDU reactor.

  • A Visual Interactive Method for Prime Implicants Identification
    IEEE Transactions on Reliability, 2015
    Co-Authors: Francesco Di Maio, Samuele Baronchelli
    Abstract:

    We propose a visual interactive method for the identification of the Prime Implicants (PIs) of dynamic non-coherent systems. Visual interactive methods integrate mathematical and symbolic models with runtime interaction and real-time graphic display, which allow visualizing the underlying physical relationships among process parameters. The proposed method is based on a parallel coordinates data mining tool that relies on an innovative pruning procedure which, on the basis of a proper selection of characteristic features of the accident sequences, retrieves the PIs among the whole set of Implicants in terms of process parameter values or component failure states or both. The method is exemplified on an artificial case study, and then applied to the dynamic reliability analysis of the Airlock System of a Canadian Deuterium Uranium reactor.

  • A Computational Framework for Prime Implicants Identification in Noncoherent Dynamic Systems
    'Wiley', 2015
    Co-Authors: Francesco Di Maio, Baronchelli Samuele, Zio Enrico
    Abstract:

    International audienceDynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., Event Trees (ETs) and Fault Trees (FTs)) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this paper, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the Prime Implicants (PIs) of the dynamic system. The framework entails adopting a Multiple-Valued Logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a Differential Evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic non-coherent system composed by five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases

  • A Computational Framework for Prime Implicants Identification in Noncoherent Dynamic Systems
    Risk Analysis, 2014
    Co-Authors: Francesco Di Maio, Samuele Baronchelli
    Abstract:

    Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., event trees [ETs] and fault trees [FTs]) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time†dependent model that includes the dependencies with the stochastic transition events. In this article, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the Prime Implicants (PIs) of the dynamic system. The framework entails adopting a multiple†valued logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a differential evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic noncoherent system composed of five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases.

Enrico Zio - One of the best experts on this subject based on the ideXlab platform.

  • A COMPUTATIONAL FRAMEWORK FOR Prime Implicants IDENTIFICATION IN NON-COHERENT DYNAMIC SYSTEMS
    2016
    Co-Authors: Francesco Di Maio, Samuele Baronchelli, Enrico Zio
    Abstract:

    Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., Event Trees (ETs) and Fault Trees (FTs)) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this paper, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the Prime Implicants (PIs) of the dynamic system. The framework entails adopting a Multiple-Valued Logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a Differential Evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic non-coherent system composed by five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases.

  • A Visual Interactive Method for Prime Implicants Identification
    IEEE Transactions on Reliability, 2015
    Co-Authors: Francesco Di Maio, Samuele Baronchelli, Enrico Zio
    Abstract:

    We propose a visual interactive method for the identification of the Prime Implicants (PIs) of dynamic non-coherent systems. Visual interactive methods integrate mathematical and symbolic models with runtime interaction and real-time graphic display, which allow visualizing the underlying physical relationships among process parameters. The proposed method is based on a parallel coordinates data mining tool that relies on an innovative pruning procedure which, on the basis of a proper selection of characteristic features of the accident sequences, retrieves the PIs among the whole set of Implicants in terms of process parameters values and/or components failure states. The method is exemplified on an artificial case study and, then, applied for the dynamic reliability analysis of the Airlock System (AS) of a CANDU reactor.

Jean Chritophe Madre - One of the best experts on this subject based on the ideXlab platform.

  • fault tree analysis 10 sup 20 Prime Implicants and beyond
    Reliability and Maintainability Symposium, 1993
    Co-Authors: Olivier Coudert, Jean Chritophe Madre
    Abstract:

    The performances of almost all available fault tree analysis tools are limited by the performance of the Prime implicant computation procedure used. All these products manipulate the Prime Implicants of the fault trees explicitly, so that their complexities are directly related to the number of Prime Implicants to be generated. The authors present a novel analysis method of coherent as well as noncoherent fault trees that overcomes this limitation because its computational cost is not related to the number of variables, gates, or Prime Implicants of these trees. The interactive fault tree analyzer MetaPrime based on this new method has been shown by experience to be able to perform in seconds the complete analysis of noncoherent fault trees with more than 10/sup 20/ Prime Implicants. >

  • Fault tree analysis: 10/sup 20/ Prime Implicants and beyond
    Annual Reliability and Maintainability Symposium 1993 Proceedings, 1993
    Co-Authors: Olivier Coudert, Jean Chritophe Madre
    Abstract:

    The performances of almost all available fault tree analysis tools are limited by the performance of the Prime implicant computation procedure used. All these products manipulate the Prime Implicants of the fault trees explicitly, so that their complexities are directly related to the number of Prime Implicants to be generated. The authors present a novel analysis method of coherent as well as noncoherent fault trees that overcomes this limitation because its computational cost is not related to the number of variables, gates, or Prime Implicants of these trees. The interactive fault tree analyzer MetaPrime based on this new method has been shown by experience to be able to perform in seconds the complete analysis of noncoherent fault trees with more than 10/sup 20/ Prime Implicants.

  • fault tree analysis 1020 Prime Implicants and beyond
    1993
    Co-Authors: Olivier Coudert, Jean Chritophe Madre
    Abstract:

    The performances of almost all available fault tree analysis tools are limited by the performance of the Prime implicant computation procedure they use. All these procedures manipulate the Prime Implicants of the fault trees explicitly, so that their complexities are directly related to the number of Prime Implicants to be generated. This paper presents a new analysis method of coherent as well as noncoherent fault trees that overcomes this limitation because its computational cost is not related to either the number of variables or the number of gates or the number of Prime Implicants of these trees. The interactive fault tree analyser METAPrime that is based on this new method has been shown by experience to be able to perform in seconds the complete analysis of noncoherent fault trees with more than 10 Prime Implicants.

  • fault tree analysis 1020 Prime Implicants and beyond
    1993
    Co-Authors: Olivier Coudert, Jean Chritophe Madre
    Abstract:

    The performances of almost all available fault tree analysis tools are limited by the performance of the Prime implicant computation procedure they use. All these procedures manipulate the Prime Implicants of the fault trees explicitly, so that their complexities are directly related to the number of Prime Implicants to be generated. This paper presents a new analysis method of coherent as well as noncoherent fault trees that overcomes this limitation because its computational cost is not related to either the number of variables or the number of gates or the number of Prime Implicants of these trees. The interactive fault tree analyser METAPrime that is based on this new method has been shown by experience to be able to perform in seconds the complete analysis of noncoherent fault trees with more than 10 Prime Implicants.

  • A new method to compute Prime and essential Prime Implicants of Boolean functions
    1992
    Co-Authors: Jean Chritophe Madre, Olivier Coudert
    Abstract:

    Computing the Prime Implicants and the essential Prime Implicants of Boolean functions is a problem that has applications in several areas of computer science, for instance it is critical in circuit synthesis and optimization, but also in automated reasoning. In this paper we propose a new method to compute implicitly the sets of Prime Implicants and of essential Prime Implicants of incompletely specified Boolean functions. This method allows us to handle functions that have sets of Prime Implicants and of essential Prime Implicants several orders of magnitude larger than those of the functions that could be handled by existing methods. The key idea that makes these computations possible is to manipulate sets of Prime and of essential Prime Implicants denoted by their meta-products, which are characteristic functions. These functions are represented with binary decision diagrams that are a very compact canonical graph representation of Boolean functions and that support very efficiently all the operations needed here.

Olivier Coudert - One of the best experts on this subject based on the ideXlab platform.

  • fault tree analysis 10 sup 20 Prime Implicants and beyond
    Reliability and Maintainability Symposium, 1993
    Co-Authors: Olivier Coudert, Jean Chritophe Madre
    Abstract:

    The performances of almost all available fault tree analysis tools are limited by the performance of the Prime implicant computation procedure used. All these products manipulate the Prime Implicants of the fault trees explicitly, so that their complexities are directly related to the number of Prime Implicants to be generated. The authors present a novel analysis method of coherent as well as noncoherent fault trees that overcomes this limitation because its computational cost is not related to the number of variables, gates, or Prime Implicants of these trees. The interactive fault tree analyzer MetaPrime based on this new method has been shown by experience to be able to perform in seconds the complete analysis of noncoherent fault trees with more than 10/sup 20/ Prime Implicants. >

  • Fault tree analysis: 10/sup 20/ Prime Implicants and beyond
    Annual Reliability and Maintainability Symposium 1993 Proceedings, 1993
    Co-Authors: Olivier Coudert, Jean Chritophe Madre
    Abstract:

    The performances of almost all available fault tree analysis tools are limited by the performance of the Prime implicant computation procedure used. All these products manipulate the Prime Implicants of the fault trees explicitly, so that their complexities are directly related to the number of Prime Implicants to be generated. The authors present a novel analysis method of coherent as well as noncoherent fault trees that overcomes this limitation because its computational cost is not related to the number of variables, gates, or Prime Implicants of these trees. The interactive fault tree analyzer MetaPrime based on this new method has been shown by experience to be able to perform in seconds the complete analysis of noncoherent fault trees with more than 10/sup 20/ Prime Implicants.

  • fault tree analysis 1020 Prime Implicants and beyond
    1993
    Co-Authors: Olivier Coudert, Jean Chritophe Madre
    Abstract:

    The performances of almost all available fault tree analysis tools are limited by the performance of the Prime implicant computation procedure they use. All these procedures manipulate the Prime Implicants of the fault trees explicitly, so that their complexities are directly related to the number of Prime Implicants to be generated. This paper presents a new analysis method of coherent as well as noncoherent fault trees that overcomes this limitation because its computational cost is not related to either the number of variables or the number of gates or the number of Prime Implicants of these trees. The interactive fault tree analyser METAPrime that is based on this new method has been shown by experience to be able to perform in seconds the complete analysis of noncoherent fault trees with more than 10 Prime Implicants.

  • fault tree analysis 1020 Prime Implicants and beyond
    1993
    Co-Authors: Olivier Coudert, Jean Chritophe Madre
    Abstract:

    The performances of almost all available fault tree analysis tools are limited by the performance of the Prime implicant computation procedure they use. All these procedures manipulate the Prime Implicants of the fault trees explicitly, so that their complexities are directly related to the number of Prime Implicants to be generated. This paper presents a new analysis method of coherent as well as noncoherent fault trees that overcomes this limitation because its computational cost is not related to either the number of variables or the number of gates or the number of Prime Implicants of these trees. The interactive fault tree analyser METAPrime that is based on this new method has been shown by experience to be able to perform in seconds the complete analysis of noncoherent fault trees with more than 10 Prime Implicants.

  • A new method to compute Prime and essential Prime Implicants of Boolean functions
    1992
    Co-Authors: Jean Chritophe Madre, Olivier Coudert
    Abstract:

    Computing the Prime Implicants and the essential Prime Implicants of Boolean functions is a problem that has applications in several areas of computer science, for instance it is critical in circuit synthesis and optimization, but also in automated reasoning. In this paper we propose a new method to compute implicitly the sets of Prime Implicants and of essential Prime Implicants of incompletely specified Boolean functions. This method allows us to handle functions that have sets of Prime Implicants and of essential Prime Implicants several orders of magnitude larger than those of the functions that could be handled by existing methods. The key idea that makes these computations possible is to manipulate sets of Prime and of essential Prime Implicants denoted by their meta-products, which are characteristic functions. These functions are represented with binary decision diagrams that are a very compact canonical graph representation of Boolean functions and that support very efficiently all the operations needed here.