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Comprehensive causal specification of asynchronous controller and arbiter behaviour.

Wollowski, R.; Beister, J.

In: Yakovlev, A.; Gomes, L.; Lavagno, L.: Hardware Design and Petri Nets, pages 3-32. Boston: Kluwer Academic Publishers, 2000.

Abstract: The topic of this paper is the precise modelling of all known forms of asynchronous controller and arbiter behaviour from a causal point of view, and for the purpose of synthesis. In addition to the causal relations between input and output edges provided by the conventional STG (dependence, independence, and exclusion) two forms of pseudo-causality, b- and tcb-concurrency (in signal-tracking behaviour), causal linkage (in multiple input changes and bursts), and race causality (temporal relations as causes, in critical input races) are found to be needed. For their Petri net representation, tc-labelled read and inhibitor arcs, transitions labelled with joint events, and decision transitions representing internal events are introduced. Based on these results, a generalized STG for the first time allows precise causal specifications of all known forms of arbiter behaviour, in particular of `three-way' arbiters that recognize and respond to simultaneous requests with a specific reaction. Several circuit examples are discussed.

Keywords: arbiters, asynchronous circuits, Petri nets, Signal Transition Graphs.

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