mapping an algorithm to systolic arrays

[ozzy_85]

i was goin thru this book, "transformational approaches to systolic design" and i came across several terms that i didn't understand. although searchin thru google and references to wikipedia have clarified a few terms, i still have a term that's giving me a lot of trouble to understand, can anybody explain what an "n-dimensional index set of an algorithm" means

regards

[hutch--]

I may be leading you astray here but usually "n" means a number so it may mean a "number-dimensional index set of an algorithm".

[Eóin]

Can you give us some more of the text that surrounded it just to get things into context.

[ozzy_85]

hutch, i did understand that n stood for a number, thankx anyway :bg, but i wanted to know the meaning of "index set of an algorithm"...

as Eoin requested, here is the text...

Most of the methods for synthesizing systolic structures consider only a systme of uniform recurrence equations. The work done by Moldovan and Fortes laid the foundation for a number systematic methods of array synthesis from uniform recurrences.

In the method due to Moldovan and Fortes, called in this chapter the dependency method, the algorithm (A) is represented as a 5-tuple (J^n,C,D,X,Y)  [guyz, i added this text within the square brackets, J^n is J raised to the power n]. J^n is a finite n-dimensional index set of A, C is the set of triples which represent the set of compuytations performed, D is the set of dependencies, X is the set of input variables and Y is the set of output variables. A feasible design is obtained by a linear transformation, represented as n x n matrix T, of the index space. Thus,

                                   T = [zS]^t    [the t indicate 'transpose']

where z is a 1 x n schedule vector and S is the processor allocation matrix. For any index point j,
S sub j [as in S subscript j] denotes the processor at which the index point executes and z sub j
is the time of execution at that processor.

from my understanding, (which may be totally of the track) i think that the index set of an algorithm is the set of all points in an algorithm that require a some processing. i might be wrong, i have no clue, that's why i thought may be i could get some expert help on this.