Recording the use of memory in right-boundary grammars and push-down automata

Summary Within the framework of coordinated pair systems a push-down automatonA is formalized as an ordered pair (G ₁,G ₂) of grammars, whereG ₁ is a right-linear grammar modelling the finite state control ofA and the reading of the input ofA, and G₂ is a right-boundary grammar modelling the push-down store ofA. In this paper we present a systematic investigation into the use of memory of right-boundary grammars. Various methods of recording the use of memory are introduced. The results presented concern regularity properties of each of the methods and the interrelationships of the records obtained by different methods. Finally the translation of these results to the level of push-down automata (coordinated pair systems) is discussed.