Towards a Formal Approach to Defining and Computing the Complexity of Component Based Software

With the rapid development of software engineering and the widely adoption of software systems in various domains, the requirement for software systems is becoming more and more complex, which results in very complex software systems. Motivated by the principle of divide and conquer, component based software development is an effective way of managing the complexity in software development. In this paper, we propose a calculus to formally describe the functional and performance specification of component based software and provide formal semantics for the proposed calculus. Then we provide a method to measure the dynamic complexity of software compositions based on the proposed calculus. Finally, we define a set of algebraic laws to manifest the complexity relations between different functionally equivalent components. We conduct a case study with a real software system and the results show that our method is able to calculate the dynamic complexity of component based systems, and the complexity can be reduced based on our algebraic laws.