Converting affine recurrence equations to quasi-uniform recurrence equations

  • Yoav Yaacoby
  • Peter R. Cappello
VLSI Testing And Derivation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 319)


Most work on the problem of synthesizing a systolic array from a system of recurrence equations is restricted to systems of uniform recurrence equations. In this paper, this restriction is relaxed to include systems of affine recurrence equations. A system of uniform recurrence equations typically can be embedded in spacetime so that the distance between a variable and a dependent variable does not depend on the problem size. Systems of affine recurrence equations which are not uniform, do not enjoy this property. A method is presented for converting a system of affine recurrence equations to an equivalent system of recurrence equations that is uniform, except for points near the boundaries of its index sets. A characterization of those systems of affine recurrence equations that can be so converted is given, along with an algorithm that decides if a system is amenable to such a conversion, and a procedure that converts those affine systems which can be converted.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Yoav Yaacoby
    • 1
  • Peter R. Cappello
    • 2
  1. 1.Electrical and Computer Engineering Dept.University of CaliforniaSanta Barbara
  2. 2.Computer Science Dept.University of CaliforniaSanta Barbara

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