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.

翻译：图灵机模拟了一种老式计算机，它无法与用户或其他计算机交互，仅能进行批处理。因此，我们提出了反应式图灵机以克服这些缺陷。在反应式图灵机中，变迁带有标签以体现交互性，在生成的过程图中我们使用互模拟等价而非语言等价。随后，我们重新审视了自动机理论与形式语言理论中的经典定理与概念。本文重点研究下推自动机与上下文无关文法之间经典对应关系。通过将顺序组合的过程算子替换为带有中间接受能力的排序算子，我们在此框架下获得了更好的对应关系。研究发现，恢复完整对应关系的关键缺失要素是引入状态感知概念。