A lattice-based framework for the classification and design of asynchronous pipelines

This paper presents a unifying framework for the modeling of asynchronous pipeline circuits. A pipeline protocol is captured in a graph-based model which defines the partial ordering of both its control and data events. The relationship between an entire space of different protocols is then captured in a semi-lattice, which has well-defined top and bottom elements, corresponding to the most concurrent and least concurrent protocol variants, respectively. This framework also provides a set of correct-by-construction transformation rules which allows for the systematic exploration of the entire design space by their successive application. To the best of our knowledge, this is the first formal framework for asynchronous pipelines which can capture protocols from a variety of logic style families, including both dynamic and static. It is also the first to provide a formal foundation for the design-space exploration of asynchronous pipelines.