## The Synthesis of Control Signals for One-Dimensional Systolic
Arrays

**Jingling Xue and Christian Lengauer**
*Abstract:* We apply a previously reported synthesis method
of control signals for systolic arrays [19]. In [19], a systolic
array is described by an index transformation expressed as a
non-singular square integer matrix, which happens to be a bijection
from Q^{n} to Q^{n}. The method expects uniform recurrence
equations (source UREs) and returns a specification of control
signals in terms of another set of UREs (control UREs); *n* is
the number of indices in the source UREs. We apply this method to
the special case of one-dimensional systolic arrays; they are
described by index transformations from Q^{n} to Q^{2}. This
requires a modification of the part of the method that depends on
the bijectivity of the space-time mapping.

*LFCS report ECS-LFCS-91-156*

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