Relativistic causality and clockless circuits

TL;DR

This paper explores the application of relativistic causality concepts to clockless delay-insensitive circuits, introducing R-traces to better model communication and causality in such systems.

Contribution

It introduces relativistic generalizations of traces (R-traces) and redefines Udding's rules, linking clockless circuit causality with relativistic causality principles.

Findings

R-traces effectively model communication in DI circuits.

Relativistic causality provides new insights into clockless circuit design.

Revised Udding's rules align with relativistic causality concepts.

Abstract

Time plays a crucial role in the performance of computing systems. The accurate modelling of logical devices, and of their physical implementations, requires an appropriate representation of time and of all properties that depend on this notion. The need for a proper model, particularly acute in the design of clockless delay-insensitive (DI) circuits, leads one to reconsider the classical descriptions of time and of the resulting order and causal relations satisfied by logical operations. This questioning meets the criticisms of classical spacetime formulated by Einstein when founding relativity theory and is answered by relativistic conceptions of time and causality. Applying this approach to clockless circuits and considering the trace formalism, we rewrite Udding's rules which characterize communications between DI components. We exhibit their intrinsic relation with relativistic causality. For that purpose, we introduce relativistic generalizations of traces, called R-traces, which provide a pertinent description of communications and compositions of DI components.