# Hierarchy of parser grammars vs Chomsky hierarchy of grammars and the comparsion of the language acceptance power of each parser grammar

While reading the text Modern Compiler Implementation in C by Andrew Appel I came across the hierarchy of grammar given below.

The above diagram is very helpful in understanding the correlation among the various parser grammars. All the grammar above are context free grammars. From theory of computation texts, I have the following Chomsky hierarchy of grammars in my mind.

Now I wonder, how to correlate these two diagrams - a possible superposition, which shall show where exactly in the Chomsky hierarchy the parser grammars lie, and their extent with respect to the boundaries already defined by Chomsky hierarchy.

If possible, could you please as well suggest the resource from which I can develop more knowledge regarding this.

PS: After the comments and discussion in the answer by Yuval Filmus, I made an attempt to draw the situation:

If we consider on the basis of the power of language corresponding to a grammar type

If we consider just on the basis of grammar type

Are the above diagrams which I have constructed as per my understanding correct? If they are not then could anyone please rectify it...

• All of the grammars in your first figure are context-free grammars, yes (I figured it out while self studying, based on the fact that since we are considering parsing, only CFGs have parse trees) but what I was actually looking for is which of the grammars in the first diagram are a part of DCFG and which are not. Which of them are regular etc... I guess I was not above to express myself properly. Sorry.. :( Sep 18, 2021 at 10:52