Empirical Studies on the Functional Complexity of Software in Large-Scale Software Systems

Abstract

Functional complexity is one of the most fundamental properties of software because almost all other software attributes and properties such as functional size, development effort, costs, quality, and project duration are highly dependent on it. The functional complexity of software is a macro-scope problem concerning the semantic properties of software and human cognitive complexity towards a given software system; while the computational complexity is a micro-scope problem concerning algorithmic analyses towards machine throughput and time/space efficiency. This paper presents an empirical study on the functional complexity of software known as cognitive complexity based on large-scale samples using a Software Cognitive Complexity Analysis Tool (SCCAT). Empirical data are obtained with SCCAT on 7,531 programs and five formally specified software systems. The theoretical foundation of software functional complexity is introduced and the metric of software cognitive complexity is formally modeled. The functional complexities of a large-scale software system and the air traffic control systems (ATCS) are rigorously analyzed. A novel approach to represent software functional complexities and their distributions in software systems is developed. The nature of functional complexity of software in software engineering is rigorously explained. The relationship between the symbolic and functional complexities of software is quantitatively analyzed.