A note on depth-first derivations (Q1065553)

It is known that the Szilard language of a context-free grammar is not necessarily context-free, while the left Szilard language is always a simple deterministic language. Depth-first derivations can be regarded as a natural extension of leftmost derivations. In this note, it is shown that the depth-first Szilard languages are simple deterministic ones. In addition, breadth-first Szilard languages are also studied. The author gives an example of a context-free grammar with the property that the associated depth-first Szilard language is not context-free.