A. Yakovlev
M. Kishinevsky
A. Kondratyev
L. Lavagno
University of Newcastle upon Tyne. 1994
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. It has its own subtypes. 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 Turing Machine and allows the modelling of non-commutative state transition behaviour in a purely causal form.