These days I think your time, the human's time, is more important than the computers.

You might think, Boy, is there a context expensive grammar out there? What's the opposite of free?

These grammars that we've been introducing describe something new context free languages.

It relates grammars to parsing, which is one of the concepts in this class.

Finite State Machines, adding a lexer that follows them automatically,

But that's an example of an application that also uses this sort of linguistic analysis perhaps a little less related to context free grammars but still in the same vein.

So in lecture, we spent a lot of time learning about context free grammars and languages.

like HTML or SQL, the language of database queries.

It handles LL. It handles LR. It handles LALR.

That line above it is the context.

The set of languages that can be described by re write rules or grammers like this are called context free languages.

Here I've written down four claims.

This is called being lazy, and it's a phenomenal virtue when you're writing programs.

Actually, they're both just concise notations for specifying possibly infinite sets of strings.

All right. So, it's another one of these puzzle like questions.

They're the actual input that we're trying to match.

Sometimes this statement is true, and sometimes it's not.

A context free grammar can capture the language a N and b N, where N is the same.

That's much more important than knowing the particular syntax for any language.

That's a good point, Peter, and the answer is yes.

These are both infinite, infinite grammars.

That's an excellent question.

In theory, you could compose it over here as well.

Nature and culture in harmony, you see, Lizzy.

Here's a new quiz. The Great Grammar Fix Up.

In particular, it's a set of strings that can be represented by a finite state machine or a regular expression.

They may get a little bit bigger, but it will totally work.

This is always true because we have our Pac Man diagram here, and also because you can take any regular language and represent it with a context free grammar.

Units 3 and 4 were relatively abstract to some degree, intentionally so.

There are a number of references to these underneath the lecture videos, but it turns out that a lot of these notions of context free grammars or generative grammars or universal grammars actually came out of psychology or linguistics or computational linguistics to help us understand human and natural language.

Is it the case that no regular languages are context free languages and vice versa?

Lets review each of these

All right. Now that you've gone to the hard work of defining all of those procedures,

It depends on the context.

This branch of the family is all about representation.

I am just gonna pause for a moment to let you think about that.

In this problem we've been asked to define a function, cfgempty, which takes in a representation of a context free grammar, a starting state, and a list of visited states and determines whether or not that context free grammar is empty.

They specify sets of strings, and they can be implemented under the hood with finite state machines.

We need to know where we came from in order to know where we're going.

This is sometimes true.

Well, because, sentences are more interesting.

A context free language is also a set of strings but can be represented by context free grammar, and what these 3 questions are asking us in this problem is to determine the relationship between a regular language and a context free language, so let's say this bubble represents the set of regular languages.

But is there anything beyond that?

Y has the value of 2.

But if right above it I've written X 0, then we'd get a different answer.