Context Free Grammars with Variables are Universally Powerful

DGL is a tool for generating test data for hardware and software, and for generating simulation input. DGL is based on probabilistic context-free grammars. To facilitate generating data in many different forms, many different types of productions are available. One can change probabilities and selection methods and perform other tasks. The most powerful type of production is the variable. Variables have a single right-hand side alternative that can be changed at run time. Combining variables with ordinary, unenhanced variables makes DGL universally powerful. This paper provides a proof of this fact. The general approach is described and is clarified using a specific, tested example.