Chapter 2: Q14E (page 156)

Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.
$A \to B A B | B | ε B \to 00 | ε$

Short Answer

Expert verified

Answer

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

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:

$A \to B C A \to a$

Add a new start symbol S

$S \to A A \to B A B | B | ε B \to 00 | ε$

Remove ε-productions.

The two ε-productions are:

$A \to ε B \to ε R e m o v e, A \to ε S \to A | ε A \to B A B | B B ⊙ 00 | ε R e m o v e B \to ε S \to A | ε A \to B A B | A B | B A | B B | B | ε B \to 00 A \to ε i s c r e a t e d a g a i n . R e m o v e A \to ε A \to B A B | B B | A B | B | B A | ε B \to 00 R e m o v e A \to ε a g a i n . S \to A | ε A \to B A B | B B | A B | B | B A B \to 00$

Remove the unit productions.

The two-unit productions are:

$S \to A R e m o v e S \to A . S \to B A B | B B | A B | B | B A | ε A \to B A B | B B | A B | B | B A B \to 00 R e m o v e S \to B . S \to B A B | B B \to | A B | 00 | B A | ε A \to B A B | B B | A B | B | B A 3 B \to 00 R e m o v e A \to B S \to B A B | B B | A B | 00 | B A | ε A \to B A B | B B | A B | 00 | B A B \to 00$

Add new variables

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

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Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.
$A \to B A B | B | ε B \to 00 | ε$

Short Answer

Step by step solution

Define Chomsky Normal Form (CNF)

Add a new start symbol S

Remove ε-productions.

Remove the unit productions.

Add new variables

One App. One Place for Learning.

Most popular questions from this chapter

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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

Remove ε-productions.

Remove the unit productions.

Add new variables

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Computer Systems

Theory of Computation

Big Data

Computer Network

Computer Programming

Algorithms in Computer Science

Study anywhere. Anytime. Across all devices.

Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.
$A \to B A B | B | ε B \to 00 | ε$