### Solution Found!

# Say that a variable A in CFL G is usable if it appears in

**Chapter , Problem 4.31**

(choose chapter or problem)

**QUESTION:**

Say that a variable A in CFL \(G\) is usable if it appears in some derivation of some string \(w \in G\). Given a CFG \(G\) and a variable \(A\), consider the problem of testing whether \(A\) is usable. Formulate this problem as a language and show that it is decidable.

### Questions & Answers

**QUESTION:**

Say that a variable A in CFL \(G\) is usable if it appears in some derivation of some string \(w \in G\). Given a CFG \(G\) and a variable \(A\), consider the problem of testing whether \(A\) is usable. Formulate this problem as a language and show that it is decidable.

**ANSWER:**

Let L be the language corresponding to the problem of testing whether a variable A in a CFG G is usable.

L = {

L is decidable since it can be checked by an algo