The Concept of Problem Complexity

Recognizing the impact of system complexity on the success of a system's development has created significant research efforts towards measuring system complexity. In particular, the research community has proposed techniques to measure three types of system complexity: (1) structural complexity, which measures the complexity resulting from physical interconnection of components; (2) functional complexity, which measures the complexity resulting from interconnection of system functions; and (3) organizational complexity, which measures the contractual interconnection of the different organizations developing the system. The majority of these metrics focus on measuring aspects of the complexity of an existing system or design. However, a metric to anticipate the complexity induced by the problem itself on a system's development is lacking. We therefore present the concept of Problem Complexity as the complexity level that a set of requirements can impose to any system fulfilling them. In addition, we mathematically demonstrate using the concept of joint entropy how problem complexity defines the minimum level of complexity a system can achieve for a given set of requirements. The paper suggests an analytic formulation to measure the complexity induced by a set of requirements in a system's development that is based on a set of heuristics that facilitate identification of conflicts between requirements. The use of such analytical formulation is showcased on a notional case-study