Pipeline-automata — A model for acyclic systolic systems

Abstract

In this paper semisystolic systems with acyclic interconnection structures are investigated. Their underlying acyclic graphs represent partially ordered set diagrams of specific partially ordered sets. To understand the nature of such systems a new kind of polyautomata is introduced which we call pipeline-automata. The dynamical behavior of a pipeline-automaton resembles that of a pipeline. After providing the necessary order theoretic concepts the abilities of pipeline-automata with respect to equivalence, isomorphy and simulation are discussed. Because of their outstanding practical relevancy pipeline-automata with grid like interconnection structures are studied. To demonstrate the power of the formalism introduced, important results about semisystolic systems are transferred into the concept of pipeline-automata. This provides also a new proof of the ”Retiming Lemma”, which is shorter and even more comprehensible than the original one from Leiserson and Saxe.