An axiomatic approach of software functionality measure

Three axioms for functional complexity of software are proposed. The first axiom asserts that functional complexity is a function and is computable at the specification level. The second axiom argues that an empty specification has zero functional complexity. The third axiom asserts that a harder specification has no less functional complexity than an easier one. With these three axioms and various definitions of the notions of functional complexity, a number of theorems are proved. Code metrics, including statement count, M. Halstead's (1977) programming effort, and T. McCabe's cyclomatic number are reviewed, together with specification metrics including L. Hellerman's (1972) metric, D. Schutt's (1977) metric, N. Coulter's (1987) metric, and A. Albrecht's (1983) functional point. These metrics are evaluated with respect to the three axioms. Results show that code metrics do not satisfy these axioms, while Hellerman, Schutt, and Coulter metrics do.<>