Synchronous approach to the functional equivalence of embedded system implementations

Design space exploration is the process of analyzing several functionally equivalent alternatives to determine the most suitable one. A fundamental question is whether an implementation is consistent with the high-level specification or whether two implementations are “equivalent.” The synchronous assumption has made it possible to develop efficient procedures for establishing functional equivalence between different implementations in the domains of synchronous circuits and synchronous reactive systems. We extend this notion to embedded systems that do not satisfy the synchronous assumption inside their boundaries but only at the interface with the environment. Leveraging this property, we define synchronous equivalence for embedded systems that strongly resembles the concept of functional equivalence for sequential circuits. We develop efficient synchronous equivalence analysis algorithms for embedded system designs. The efficiency comes from analyzing the behavior statically on abstract representations, at a cost that some of the negative results may be false, i.e. the analysis is conservative. We develop primitives for making the representation more/less abstract, trading off complexity of the algorithms with the conservativeness of the results. We apply our analysis algorithms to an ATM switch and demonstrate that synchronous equivalence opens design exploration avenues uncharted before.