Temporal State Machines: Using temporal memory to stitch time-based graph computations

TL;DR

This paper introduces a systematic framework combining tropical algebra and temporal memory to design generalized race logic circuits, enabling efficient, energy-saving time-based graph computations like Dijkstra's algorithm.

Contribution

It develops a formal mathematical framework for race logic using tropical algebra and demonstrates a temporal state machine implementation with memristor-based memory.

Findings

Successfully implemented a temporal state machine for Dijkstra's algorithm

Achieved energy and throughput improvements over traditional methods

Provided a generalizable approach for time-based graph computations

Abstract

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.