Chapter 2: Q9E (page 155)

Give a context-free grammar that generates the language
$A = {a^{i} b^{j} k^{k} i = j o r j = k w h e r e i, j, k \geq 0}$
Is your grammar ambiguous? Why or Why not?

Short Answer

Expert verified

Context-free grammar:

$\begin{array}{rcl} S & \to & T_{a b} C A T_{b c} \\ T_{a b} & \to & a T_{a b} b ε \\ T_{b c} & \to & b T_{b c} c ε \\ C & \to & C c ε \\ A & \to & A a ε \end{array}$

The grammar is ambiguous, because a string can be derived in more than one way.

Step by step solution

Explain context-free grammar

Context-free grammar is the set of rules that are used to recognize the context-free language. The context-free grammar contains the production rules, variables, and terminals.

Provide example of context-free grammar

Consider the given language

$A = \{a^{i} b^{j} c^{k} i = j o r j = k w h e r e i, j, k \geq 0\}$ , The context-free grammar for the given language can be derived as follows:

$\begin{array}{rcl} S & \to & T_{a b} C A T_{b c} \\ T_{a b} & \to & a T_{a b} b ε \\ T_{b c} & \to & b T_{b c} c ε \\ C & \to & C c ε \\ A & \to & A a ε \end{array}$

Consider the string $ε$ ; it can be derived in more than one way. By choosing the T_abC , and substituting T_ab by $ε$ , C by $ε$ . In other way, AT_bc can be chosen, and substituting A by $ε$ , T_bc by $ε$ .

Therefore, the grammar is ambiguous, because a string can be derived in more than one way.

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Give a context-free grammar that generates the language
$A = {a^{i} b^{j} k^{k} i = j o r j = k w h e r e i, j, k \geq 0}$
Is your grammar ambiguous? Why or Why not?

Short Answer

Step by step solution

Explain context-free grammar

Provide example of context-free grammar

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Give a context-free grammar that generates the languageA={aibjkki=jorj=kwherei,j,k≥0}Is your grammar ambiguous? Why or Why not?

Short Answer

Step by step solution

Explain context-free grammar

Provide example of context-free grammar

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Data Representation in Computer Science

Algorithms in Computer Science

Computer Systems

Computer Programming

Big Data

Computer Network

Study anywhere. Anytime. Across all devices.

Give a context-free grammar that generates the language
$A = {a^{i} b^{j} k^{k} i = j o r j = k w h e r e i, j, k \geq 0}$
Is your grammar ambiguous? Why or Why not?