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

Chapter , Problem 4.31

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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.

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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 = { | A is usable in G from w}

L is decidable since it can be checked by an algo

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