From System Requirements to Software Requirements in the Four-Variable Model

The four-variable model of software-controlled embedded systems originally proposed by Parnas and Madey has been used successfully in the development of safety-critical applications in various industries. The model does not explicitly specify the software requirements, but rather bounds them by specifying the system requirements and the input and output hardware interfaces of the system. The software engineers are left with the problem of how to construct software that satisfies the system requirements and hardware interfacing constraints. After formalizing the properties of acceptable system and software implementations using the demonic calculus of relations, we provide (i) a necessary and sufficient condition for the existence of an acceptable software implementation and (ii) a mathematical characterization of the software requirements in terms of their weakest specification.