TABLE OF CONTENTS The difficulty in calculating system properties from component properties can be illustrated by a simple example. Imagine two software components used in series. The first component receives the system input, does its calculation, and invokes the second component, so its output is the second component s input. The second component does its calculation on input received from the first, and its output is the system output. Consider the performance property of this composite system. To use the paradigm that has been successful in other engineering disciplines, one wants to measure the run time of each component in isolation, say T 1 and T 2, and then calculate the system run time T=T 1 +T 2.
Assuming each component s run time is the same for all inputs, this calculation will be correct. However, the assumption is very unlikely to hold usually, component run times vary with input. In principle, there is no difficulty. The run times are actually functions of the input, say represented by a single variable x. Then T(x)=T 1 (x)+ T 2 (x'), where x ? is the output of the first component on its input x. Unfortunately, the functional values of T 1, T 2, and x ? are seldom available in practice. The approach from first principles is precisely that of proving and composing functional properties of programs, an approach that has proven impractical. For practical calculations, some kind of testing and...
