# Pushdown Automata and Context-Free Grammars in Bisimulation Semantics

arXiv: https://arxiv.org/abs/2203.01713 · HTML: https://mlsanity.com/paper/2203.01713/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [Finding path and cycle counting formulae in graphs with Deep Reinforcement Learning](https://mlsanity.com/paper/2410.01661/) (2024)

## Abstract (arXiv)

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.