An approach to testing the nonexistence of initial state in Z specifications

Formal methods use a mathematically based notation to describe the specification of software systems and, based on these they have a notation of an implementation satisfying a specification. Z notation has been widely used in academia and industry. One of the things that we have either to prove formally, or to convince ourselves of in some other way, about every specification written in Z, is that the initial state exists. This paper explores theoretically the test of initial states in Z specifications. The new concepts, constructed function and constrained state space are introduced. The testing approach proposed in this paper can be used to detect the erroneous initial state in Z specifications. By way of examples, the application of testing approach is given.