Practice - Union
Practice Questions
Test your understanding with targeted questions
Define the term 'Union' in the context of formal languages.
💡 Hint: Think of how you would combine sets of items.
Do CFLs stay within their class when united? Explain.
💡 Hint: Recall the definition of closure properties.
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Interactive Quizzes
Quick quizzes to reinforce your learning
The union of two CFLs is a CFL. Is this statement True or False?
💡 Hint: Reflect on the definition of closure.
What operation would you use to combine L1 and L2?
💡 Hint: Think about how you would describe both languages' coverage.
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Challenge Problems
Push your limits with advanced challenges
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.
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
Supplementary resources to enhance your learning experience.