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Consider the languages L1={0m1m0n|m,n>0}, L2={0m1n0n|m,n>0} and L = L1 ∪ L2 over the alphabet {0,1}. Which of the following statements is/are true?
I. L is unambiguous.
II. L is inherently ambiguous.
III. L can be recognized by a PDA..
IV. L can be recognized by a DPDA.
  • a)
    I and III
  • b)
    II and III
  • c)
    I and IV
  • d)
    II and IV
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the languagesL1={0m1m0n|m,n>0}, L2={0m1n0n|m,n>0}and L ...
L1 and L2 are context free languages. Hence, L is also context free, recognized by some
push-down automaton, because CFL's are closed under Union.
The subset {0n1n0n|n⟩0} of L is the set of strings that has two distinct derivations:
one coming from L1, and the other coming from L2. It turns out that every grammar
that describes L will remain ambiguous for at least some strings of the form 0n0n0n 
Hence, L is inherently ambiguous.
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Most Upvoted Answer
Consider the languagesL1={0m1m0n|m,n>0}, L2={0m1n0n|m,n>0}and L ...
L1 is the language of all strings of the form 0^m1^m0^n, where m and n are non-negative integers.
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Consider the languagesL1={0m1m0n|m,n>0}, L2={0m1n0n|m,n>0}and L = L1∪ L2over the alphabet {0,1}. Which of the following statements is/are true?I. L is unambiguous.II. L is inherently ambiguous.III. L canberecognized by a PDA..IV. Lcan berecognized by a DPDA.a)I and IIIb)II and IIIc)I and IVd)II and IVCorrect answer is option 'B'. Can you explain this answer?
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