The theory of acyclic systolic systems

Abstract

The topic of this paper is the investigation of semisystolic systems with acyclic interconnection structure. To understand the nature of such systems, a new kind of polyautomaton is introduced which we call pipeline automaton. We study the abilities of pipeline automata with respect to equivalence, isomorphy, and simulation. As a major result a structure theorem concerning the simulation of n-dimensional systolic arrays is proved. From this theorem we derive a method of transforming systolic arrays producing results at the end of each computation into on-the-fly systolic arrays. Important results concerning semisystolic systems like the “Retiming Lemma,” the “Cut Theorem,” and related theorems are transferred into the context of pipeline automata. The acyclic versions of these theorems can be stated for autonomous systems excluding the I/O behavior with respect to some host computer. Thus large-scale I/O considerations can be omitted. Furthermore these statements can be proved more elegantly within an order-theoretic framework.