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In my homework we're given the following problem: Determine whether the context-free language described by the following grammar is regular, showing all the reasoning steps:

S -> T T | U

T -> 0 T | T 0 | #

U -> 0 U 0 0 | #.

My teacher says the pound sign (#) is just a delimiter that is in the alphabet and not epsilon.

I understand the order of operations here is to go from CFG --> CFL --> RL (if possible).
My problem is that I don't know how to provide a CFL given a CFG, and further, determine whether a CFL is regular.

So to ask the questions:

how do you provide a context-free language (CFL) given a context-free grammar (CFG)?

how do you determine if a context-free language (CFL) is also a regular language (RL)?

RebelOfBabylon
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$$\begin{align}L(T) &= \{0^*\#0^*\} \\ L(U) &= \{0^n\#0^{2n}\} \\ L(S) &= L(T) \circ L(T) \cup L(U) \end{align}$$ Where $\circ$ is concatenation. Clearly, $L(U)$ is not regular. What does that say about $L(S)$? How does $L(T)$ affect this?

Karolis Juodelė
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