  The Turing machine models an old-fashioned computer, that does not interact
with the user or with other computers, and only does batch processing.
Therefore, we came up with a Reactive Turing Machine that does not have these
shortcomings. In the Reactive Turing Machine, transitions have labels to give a
notion of interactivity. In the resulting process graph, we use bisimilarity
instead of language equivalence.
  Subsequently, we considered other classical theorems and notions from
automata theory and formal languages theory. In this paper, we consider the
classical theorem of the correspondence between pushdown automata and
context-free grammars. By changing the process operator of sequential
composition to a sequencing operator with intermediate acceptance, we get a
better correspondence in our setting. We find that the missing ingredient to
recover the full correspondence is the addition of a notion of state awareness.
