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On the models for asynchronous circuit behaviour with OR causality

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Abstract

Asynchronous circuits behave like concurrent programs implemented in hardware logic. The processes in such circuits are synchronised in accordance with the dynamic logical and causal conditions between switching events. The classical paradigm, easily represented in most process-oriented languages for concurrent systems modelling, is AND causality, which is often associated with a rendez-vous synchronisation. In this paper we investigate a different, less known paradigm, called OR causality. This paradigm is however different from the classical MERGE paradigm, which is based on mutually exclusive events. Petri nets and Change Diagrams provide adequate modelling and circuit synthesis tools for the various OR causality types, yet they do not always bring the specifier to a unique decision about which modelling construct must be used for which type. We present a unified descriptive tool, called Causal Logic Net, which is graphically based on Petri net but has an explicit logic causality annotation for transitions. It is aimed as the least possible generalisation of Petri nets and Change Diagrams. The signal-transition interpretation of this tool is analogous to, but more powerful than, the well-known Signal Transition Graph. A number of examples demonstrate the usefulness of this model in the synthesis of asynchronous control circuits. It is shown that the extension of the basic, unconditional, firing rule with the one that depends upon the marking of the transition preconditions increases the descriptive power of the model to that of the Turing Machine model and allows the modelling of non-commutative state transition behaviour in a purely causal form.

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Authors and Affiliations

  1. Department of Computing Science, University of Newcastle upon Tyne, NE1 7RU, England

    Alexandre Yakovlev

  2. Department of Computer Hardware, The University of aizu, 965-80, Aizu-Wakamatsu, Japan

    Michael Kishinevsky & Alex Kondratyev

  3. Dipartimento di Elettronica, Politecnico di Torino, 10129, Torino, Italy

    Luciano Lavagno

  4. Department of Computing Science, University of Newcastle upon Tyne, NE1 7RU, England

    Marta Pietkiewicz-Koutny

Authors
  1. Alexandre Yakovlev
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  2. Michael Kishinevsky
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  3. Alex Kondratyev
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  4. Luciano Lavagno
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  5. Marta Pietkiewicz-Koutny
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Yakovlev, A., Kishinevsky, M., Kondratyev, A. et al. On the models for asynchronous circuit behaviour with OR causality. Form Method Syst Des 9, 189–233 (1996). https://doi.org/10.1007/BF00122082

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  • DOI: https://doi.org/10.1007/BF00122082

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