31




 Define the function index range as:

 L = M

 U = A.(N)-(A.-M)

 A = A.
 1

where N and A. are positive constant integers, M a constant integer.

Define the variable index range (it is only with the range that the

problem can occur) as:

 L = aL.+(l-a)i+ki aE{O,l}

 U. = bU.+(1-b)i+k." bc{O,1}
 3 2 3
 A = A.
 3 2
where k. and k .u are integers and A. is a positive integer, again all
 3 3 3
constants.

 Theorem: If A. = A. there is no acceleration of variables.
 3 1
 Proof: Assume A. = A.. The number of functions is:
 j 1
 A.(N)-(A .-M)-M
 Hf A.
 1

 = N

The number of variables

 U. -L.
 n= max min +1
 v A.

 U.
 U3max =bU,+(1-b)imax+k.u
 i 3
 but imax = U. so,

 U = bU +(l-b) U+k .
 gmax 2 2 g
 = U .+k, .

 similarly,

 L = L .+k .'
 rmin J 7