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Consider the language L = {an |n ≥ 0} ∪ {anbn| n ≥ 0} and the following statements.
I. L is deterministic context-free.
II. L is context-free but not deterministic context-free.
III. L is not LL(k) for any k.
Which of the above statements is/are TRUE?
  • a)
    I only
  • b)
    II only
  • c)
    I and III only
  • d)
    III only
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider the language L = {an|n ≥ 0} ∪ {anbn| n ≥ 0} and the...
Concept:
Union of a Regular language and a Deterministic Context Free Language (DCFL) is a DCFL.
Explanation:
Statement I: TRUE.
L = {an |n ≥ 0} ∪ {anbn| n ≥ 0}
{an |n ≥ 0} is a regular language and {anbn| n ≥ 0} is a DCFL and hence, there Union would be a DCFL.
Statement II: FALSE.
L is DCFL then it is CFL too.
Statement III: TRUE
L cannot be LL(k) for any number of look-ahead. LL(k) cannot conclusively distinguish that whether the string to be parsed is from aor from anbn. Both have a common prefix.
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Community Answer
Consider the language L = {an|n ≥ 0} ∪ {anbn| n ≥ 0} and the...
The language L = {an|n < 5}="" is="" a="" regular="" language.="" 5}="" is="" a="" regular="" />
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Consider the language L = {an|n ≥ 0} ∪ {anbn| n ≥ 0} and the following statements.I. L is deterministic context-free.II. L is context-free but not deterministic context-free.III. L is not LL(k) for any k.Which of the above statements is/are TRUE?a)I onlyb)II onlyc)I and III onlyd)III onlyCorrect answer is option 'C'. Can you explain this answer?
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