Synthesis of systolic algorithms and processor arrays

  • Nikolay Petkov Turkedjiev
Nonnumerical Algorithms (Session 2.2)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)


A formal definition of a systolic array and a systolic algorithm is given. The design of a systolic array and the necessary input-output relations for a given computational problem include the design of an algorithm expressed in terms of a functional graph as an intermediate level. A discipline is introduced in the design process by identifying the features of a class of algorithms which can be embedded in systolic arrays. Cluster-homogeneous functional graphs with cluster-independent data dependences are shown to represent systolic algorithms. The proof of the theorem given is a realization procedure at the same time. The approach used is illustrated on the 1-D-convolution. The transformations used to obtain different designs are more general than those used elsewhere /4/ and have a larger field of application. The set of the linear 1-D systolic designs for the 1-D-convolution is shown to be enumerable and the different designs are grouped together in 7 classes and 42 groups (36 in case of symmetry in two of the classes). A minimal (in some sense) design can be given for each of the 42 groups. Eight of these designs, however, were given by H. T. Kung elsewhere /3/.


Systolic Array Cluster Graph Processor Array Delay Element Functional Graph 
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  1. /1/.
    Harao, M., Lomtong, P.: A cellular reconfigurable data flow computing system. PARCELLA 84, Berlin, Sept. 84. Akademie-Verlag, Berlin 1985, pp.63–72.Google Scholar
  2. /2/.
    Petkov-Turkedjiev, N.: Beitrag zur Synthese systolischer Algorithmen und Prozessorfelder. Dissertation A, TU Dresden, 1986.Google Scholar
  3. /3/.
    Kung, H.T.: Why systolic architectures. Computer (IEEE) 15 (1981) 1, pp. 37–46.Google Scholar
  4. /4/.
    Moldovan,D.I.: On the design of algorithms for VLSI systolic arrays. Proc. IEEE 71 (1983).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Nikolay Petkov Turkedjiev
    • 1
  1. 1.Technische Universität Dresden Sektion InformationstechnikDresden

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