  In this paper we give a definition of "algorithm," "finite algorithm,"
"equivalent algorithms," and what it means for a single algorithm to dominate a
set of algorithms. We define a derived algorithm which may have a smaller mean
execution time than any of its component algorithms. We give an explicit
expression for the mean execution time (when it exists) of the derived
algorithm. We give several illustrative examples of derived algorithms with two
component algorithms. We include mean execution time solutions for
two-algorithm processors whose joint density of execution times are of several
general forms. For the case in which the joint density for a two-algorithm
processor is a step function, we give a maximum-likelihood estimation scheme
with which to analyze empirical processing time data.
