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1. Let Σ = {a,b}. Give a context-free grammar that generate the following language: {a¹b²i+k : k ≥ 2,i ≥ 1} + {ai+kô²i : i,k ≥ 0} 2. The following grammar generates exactly all the strings of balanced brackets: SSS S→ (S) The (sole) nonterminal S is the start symbol of the grammar. (a) Show that this grammar is ambiguous. (b) Is this language inherently ambiguous? State your thoughts one way or another (you only need to provide your thoughts, not a proof). 3. Design a deterministic pushdown automaton that recognizes the language : {a²ibka² i,k≥ 1} Draw a table that traces the behavior of your pushdown automaton on the input aaaabbaa and explain how this input is accepted or rejected (as the case might be). 4. Is the language L = {a²ibic²idi : i, j ≥ 0} context-free? Prove one way or another.

1. Let Σ = {a,b}. Give a context-free grammar that generate the following language: {a¹b²i+k : k ≥ 2,i ≥ 1} + {ai+kô²i : i,k ≥ 0} 2. The following grammar generates exactly all the strings of balanced brackets: SSS S→ (S) The (sole) nonterminal S is the start symbol of the grammar. (a) Show that this grammar is ambiguous. (b) Is this language inherently ambiguous? State your thoughts one way or another (you only need to provide your thoughts, not a proof). 3. Design a deterministic pushdown automaton that recognizes the language : {a²ibka² i,k≥ 1} Draw a table that traces the behavior of your pushdown automaton on the input aaaabbaa and explain how this input is accepted or rejected (as the case might be). 4. Is the language L = {a²ibic²idi : i, j ≥ 0} context-free? Prove one way or another.

C++ for Engineers and Scientists
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter12: Adding Functionality To Your Classes
Section12.5: Virtual Functions
Problem 5E
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1. Let Σ = {a,b}. Give a context-free grammar that generate the following language: {a¹b²i+k : k ≥ 2,i ≥ 1} + {ai+kô²i : i,k ≥ 0} 2. The following grammar generates exactly all the strings of balanced brackets: SSS S→ (S) The (sole) nonterminal S is the start symbol of the grammar. (a) Show that this grammar is ambiguous. (b) Is this language inherently ambiguous? State your thoughts one way or another (you only need to provide your thoughts, not a proof). 3. Design a deterministic pushdown automaton that recognizes the language : {a²ibka² i,k≥ 1} Draw a table that traces the behavior of your pushdown automaton on the input aaaabbaa and explain how this input is accepted or rejected (as the case might be). 4. Is the language L = {a²ibic²idi : i, j ≥ 0} context-free? Prove one way or another.
Transcribed Image Text:1. Let Σ = {a,b}. Give a context-free grammar that generate the following language: {a¹b²i+k : k ≥ 2,i ≥ 1} + {ai+kô²i : i,k ≥ 0} 2. The following grammar generates exactly all the strings of balanced brackets: SSS S→ (S) The (sole) nonterminal S is the start symbol of the grammar. (a) Show that this grammar is ambiguous. (b) Is this language inherently ambiguous? State your thoughts one way or another (you only need to provide your thoughts, not a proof). 3. Design a deterministic pushdown automaton that recognizes the language : {a²ibka² i,k≥ 1} Draw a table that traces the behavior of your pushdown automaton on the input aaaabbaa and explain how this input is accepted or rejected (as the case might be). 4. Is the language L = {a²ibic²idi : i, j ≥ 0} context-free? Prove one way or another.
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