Optimal Parenthesization of Lexical Orderings for Dsp Block Diagrams1

Minimizing memory requirements for program and data are critical objectives when synthesizing software for embedded DSP applications. Previously, it has been demonstrated that for graphical programs based on the widely-used synchronous dataflow model, an important class of minimum code size implementations can be viewed as parenthesizations of lexical orderings of the computational blocks. Such a parenthesization corresponds to the hierarchy of loops in the software implementation. In this paper, we present a dynamic programming technique for constructing a parenthesization that minimizes data memory cost from a given lexical ordering of a synchronous dataflow graph. For graphs that do not contain delays, this technique always constructs a parenthesization that has minimum data memory cost from among all parenthesizations for the given lexical ordering. When delays are present, the technique may make refinements to the lexical ordering while it is computing the parenthesization, and the data memory cost of the result is guaranteed to be less than or equal to the data memory cost of all valid parenthesizations for the initial lexical ordering.