Abstract
Algorithms designed for VLSI implementation are commonly described by directed graphs, in which the nodes represent functional units and the arcs indicate communication links. We give a denotational semantics for such a graph in terms of the least fixed point of a set of (mutually recursive) function definitions, describing the outputs produced at each node as a function of time. This semantics is consistent with the conventional clocked operational semantics of the system. A retiming is a systematic modification of the internode delays of a design, often used to convert an algorithm design into a systolic form. The utility of such retimings in optimizing the behavior of designs is well known. We use fixed-point semantics to provide simple proofs of the correctness of certain retiming transformations from the literature and to justify other design transformations such as pipelining.
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Brookes, S. Using fixed-point semantics to prove retiming lemmas. Form Method Syst Des 2, 73–91 (1993). https://doi.org/10.1007/BF01383944
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DOI: https://doi.org/10.1007/BF01383944