Pushdown Automata and Context-Free Grammars in Bisimulation Semantics

03/03/2022
by   Jos C. M. Baeten, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/13/2023

Parallel Pushdown Automata and Commutative Context-Free Grammars in Bisimulation Semantics (Extended Abstract)

A classical theorem states that the set of languages given by a pushdown...
research
09/09/2020

Ties between Parametrically Polymorphic Type Systems and Finite Control Automata

We present a correspondence and bisimulation between variants of paramet...
research
12/22/2022

Real-valued affine automata compute beyond Turing machines

We show that bounded-error affine finite automata recognize uncountably ...
research
05/10/2023

Finitely Presentable Higher-Dimensional Automata and the Irrationality of Process Replication

Higher-dimensional automata (HDA) are a formalism to model the behaviour...
research
10/29/2018

On the Power of Quantum Queue Automata in Real-time

This paper proposed a quantum analogue of classical queue automata by us...
research
07/30/2019

Lecture Notes on Automata, Languages, and Grammars

These lecture notes are intended as a supplement to Moore and Mertens' T...
research
08/29/2022

Constructive Many-one Reduction from the Halting Problem to Semi-unification (Extended Version)

Semi-unification is the combination of first-order unification and first...

Please sign up or login with your details

Forgot password? Click here to reset