Chapter 2: 14E (page 156)

Question: Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.
$\begin{array}{l} A \to B A B | B | ε \\ B \to 00 | ε \end{array}$

Short Answer

Expert verified

$S \to B D | B B | A B | C C | B A | ε A \to B D | B B | A B | C C | B A B | C C C | 0 D \to A B$

Step by step solution

Define Chomsky Normal Form (CNF)

In theory of computation, context free grammar (CFG) generates the possible strings in a language. CFG is in Chomsky normal form (CNF) if the production rules in it are of the following forms:

A $\to$ BC

A $\to$ a

Add a new start symbol S

S $\to$ A

A $\to$ BAB | B | $ε$

B $\to$ 00 | $ε$

Step 3: Remove ε-productions.

A $\to$ $ε$

$B \to ε R e m o v e, A \to ε S \to A | ε A \to B A B | B B | B B R 00 | ε R e m o v e B \to ε S \to A | ε$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Computer Science Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Question: Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.
$\begin{array}{l} A \to B A B | B | ε \\ B \to 00 | ε \end{array}$

Short Answer

Step by step solution

Define Chomsky Normal Form (CNF)

Add a new start symbol S

Step 3: Remove ε-productions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Databases

Data Structures

Game Design in Computer Science

Theory of Computation

Computer Programming

Computer Organisation and Architecture

Study anywhere. Anytime. Across all devices.

Question: Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.A→BAB|B|εB→00|ε

Short Answer

Step by step solution

Define Chomsky Normal Form (CNF)

Add a new start symbol S

Step 3: Remove ε-productions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Databases

Data Structures

Game Design in Computer Science

Theory of Computation

Computer Programming

Computer Organisation and Architecture

Study anywhere. Anytime. Across all devices.

Question: Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.
$\begin{array}{l} A \to B A B | B | ε \\ B \to 00 | ε \end{array}$