Chapter 4: Q4E (page 193)

Let $A ε_{CFG} = {<G> | G is a CFG that generates ε}$ . Show that $A ε_{CFG}$ is decidable.

Short Answer

Expert verified

It can be shown that $A ε_{CFG}$ is decidable.

Step by step solution

Explain context-free grammar

Context-free grammar generates the context-free languages by using the production rules. The context-free grammars has the productions that has the variables and terminals.

Show that AεCFG is decidable

Convert the context-free grammar $G$ into an equivalent $G'$ CNF that is represented by the Turing machine $S$ . Construct the Turing machine $M$ that decides $A ε_{CFG}$ .

$M ='' On input <G>$ where $G$ is a context-free grammar.

Run the Turing machine $S$ on input $<G, ε>$ , where $A ε_{CFG}$ is decided by the Turing Machine $S$ .
If $S$ accepts, accept.
If $S$ rejects, reject.

Therefore, It has been shown that $A ε_{CFG}$ is decidable.

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Let $A ε_{CFG} = {<G> | G is a CFG that generates ε}$ . Show that $A ε_{CFG}$ is decidable.

Short Answer

Step by step solution

Explain context-free grammar

Show that AεCFG is decidable

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Let AεCFG={G|G is a CFG that generatesε}. Show thatAεCFGis decidable.

Short Answer

Step by step solution

Explain context-free grammar

Show that AεCFG is decidable

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Theory of Computation

Data Structures

Big Data

Issues in Computer Science

Functional Programming

Game Design in Computer Science

Study anywhere. Anytime. Across all devices.

Let $A ε_{CFG} = {<G> | G is a CFG that generates ε}$ . Show that $A ε_{CFG}$ is decidable.