Theory of Software Testing With Persistent State

Software testing began as an empirical activity, and remains part of engineering practice without a widely accepted theoretical foundation. The overwhelming majority of test methods are designed to find software errors, termed faults, in program source code, but not to assess software operational quality. To go beyond fault-seeking requires a theory that relates static program properties to executions. In the 1970s and 1980s, Gerhart, Howden, and others developed a sound functional theory of program testing. Then Duran and others used this theory to precisely define the notions of random testing and operational reliability. In the Gerhart-Howden-Duran theory, a program's behavior is a pure input-output mapping. This paper extends the theory to include persistent state, by adding a state space to the input space, and a state mapping to a program's output mapping. The extended theory is significantly different because test states, unlike inputs, cannot be chosen arbitrarily. The theory is used to analyze state-based testing methods, to examine the practicality of reliability assessment, and to suggest experiments that would increase understanding of the statistical properties of software.