Algebraic approach to time borrowing

Abstract

Abstract. This paper is about a novel application of linear algebra to the timing of digital hardware. In particular we describe a rigorous, algorithmic approach to 'time borrowing'. Time borrowing is a technique whereby the use of a multiphase clock can allow for a more flexible, efficient use of time. In this approach the system is clocked periodically, but within each clock cycle processes are allowed to interact asynchronously allowing longer processes to be juxtaposed with shorter processes. We show that this problem can be solved completely using linear algebra defined over the max-plus semi-ring, and that the method so obtained conforms with an earlier, heuristic approach to the problem.

A Max-Plus Model of Asynchronous Cellular Automata

“…This name (along with the later timing dependency graph) is inspired by its use in another novel application of Rmax to the timing of digital hardware in[21].…”