Convert Context-Free Grammar to Automata

Question

I am trying to convert the following grammar to an automata:

Let $S$ be the start symbol.

1. $S \to aQc$
2. $Q \to aQc$
3. $Q \to aaRbb$
4. $R \to aaRbb$
5. $R \to \epsilon$.

But I don't fully understand how to convert these types of grammar. Is there some steps I can follow in understanding the process?

How do I go about converting this grammar to an automata?

Answer 1

showing that every grammar has a matching PDA is actually very simple by constructing a PDA that nonderministically goes through all the possible productions of the grammar.

Given G = (V,T,P,S), define M = ({q},T,TUV,δ,q,S,{}) (notice only one state is needed).

Define δ:

For each variable A in V, δ(q, ε, A) = {(q, α)|A → α is a production of P }.

For each terminal a in T, δ(q, a, a) = {(q, ε)}.

With this, your problem is solved.

This is the standard construction shown when proving one direction of the equivalence of PDA’s and CGF’s, so finding more info should be very easy.