  Race logic, an arrival-time-coded logic family, has demonstrated energy and
performance improvements for applications ranging from dynamic programming to
machine learning. However, the ad hoc mappings of algorithms into hardware
result in custom architectures making them difficult to generalize. We
systematize the development of race logic by associating it with the
mathematical field called tropical algebra. This association between the
mathematical primitives of tropical algebra and generalized race logic
computations guides the design of temporally coded tropical circuits. It also
serves as a framework for expressing high level timing-based algorithms. This
abstraction, when combined with temporal memory, allows for the systematic
generalization of race logic by making it possible to partition feed-forward
computations into stages and organizing them into a state machine. We leverage
analog memristor-based temporal memories to design a such a state machine that
operates purely on time-coded wavefronts. We implement a version of Dijkstra's
algorithm to evaluate this temporal state machine. This demonstration shows the
promise of expanding the expressibility of temporal computing to enable it to
deliver significant energy and throughput advantages.
