Pipeline-automata — A model for acyclic systolic systems

  • Karl-Heinz Zimmermann
Submitted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 342)


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.


Interconnection Structure Order Isomorphism Positive Valuation Systolic Algorithm Local Transition Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Abbott, J.C.: Sets, Lattices and Boolean Algebras, Allyn & Bacon Inc., Boston, 1969.Google Scholar
  2. [2]
    Kung, H.T.: Why Systolic Architectures?, Computer Magazine 15 (1982), 37–46.Google Scholar
  3. [3]
    Kung, H.T.; Lam, M.S.: Wafer-Scale Integration and Two-Level Pipelined Implementations of Systolic Arrays, Journal of Parallel and Distributed Computing 1 (1984), 32–63.Google Scholar
  4. [4]
    Kung, S.-Y.; Arun, K.S.: Wavefront Array Processor: Language, Architecture and Applications, IEEE Transactions on Computers C-31 (1982), 1054–1065.Google Scholar
  5. [5]
    Lee, R.C.T.; Yang, C.B.: The Mapping of 2-D Array Processors to 1-D Array Processors, Parallel Computing 3 (1986), 217–229.MathSciNetGoogle Scholar
  6. [6]
    Leiserson, C.E.; Saxe, J.B.: Optimizing Synchronous Systems, Journal of VLSI and Computer Systems 1 (1983), 41–68.Google Scholar
  7. [7]
    Seitz, C.S.: Concurrent VLSI Architectures, IEEE Transactions on Computers C-33> (1984), 1247–1265.Google Scholar
  8. [8]
    Zimmermann, K.-H.: Acyclic Systolic Systems and Their Verification, Preprint, submitted to Journal of Parallel and Distributed Computing, 1988.Google Scholar
  9. [9]
    Zimmermann, K.-H.: Pipeline-Automaten, Arbeitsberichte des Instituts für Mathematische Maschinen und Datenverarbeitung der Universität Erlangen-Nürnberg 20, Erlangen, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Karl-Heinz Zimmermann
    • 1
  1. 1.Mathematical InstituteUniversity of BayrouthBayrouthFRG

Personalised recommendations