Practice Union (5.3.1.1) - Context-Free Grammars (CFG) and Languages - Theory of Computation
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Union

Practice - Union

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Practice Questions

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Question 1 Easy

Define the term 'Union' in the context of formal languages.

💡 Hint: Think of how you would combine sets of items.

Question 2 Easy

Do CFLs stay within their class when united? Explain.

💡 Hint: Recall the definition of closure properties.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

The union of two CFLs is a CFL. Is this statement True or False?

True
False

💡 Hint: Reflect on the definition of closure.

Question 2

What operation would you use to combine L1 and L2?

Concatenation
Union
Intersection

💡 Hint: Think about how you would describe both languages' coverage.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Propose two context-free languages with different characteristics. Show how their union is context-free by constructing the respective grammar.

💡 Hint: Remember to keep the non-terminal sets disjoint.

Challenge 2 Hard

Consider the languages L1 = { x ∈ {a,b}* | x is a palindrome } and L2 = { x | x contains the substring 'ab' }. Examine their union and discuss why it may or may not remain a CFL.

💡 Hint: Analyze the complexity of palindromic structure.

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Reference links

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