= Context Free Grammar =

Def: For every ContextFreeLanguage there is a ContextFreeGrammar that generates it and a PushDownAutomata that recognizes it.

A context-free grammar is a 4-tuple $$(V,\Sigma,R,S)$$, where

	1. Element $$V$$$ is a finite set called the variables,
	1. Element $$\Sigma$$ is a finite set, disjoint from $$V$$, called the terminals,
	1. Element $$R$$ is a finite set of rules, with each rule being a variable and a string of variables and terminals, and
	1. Element $$S \in V$$ is the start variable

An example of a rule is 

$$A \rightarrow aBa$$
$$B \rightarrow \epsilon$$