GATE Exam > GATE Questions > Consider the languages L1={wwR∣w∈{0,1}∗}L2={...
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Consider the languages L1={wwR∣w∈{0,1}∗}
L2={w#wR∣w∈{0,1}∗}, where # is a special symbol
L3={ww∣w∈(0,1}∗)
Which one of the following is TRUE?
- a)L1 is a deterministic CFL
- b)L2 is a deterministic CFL
- c)L3 is a CFL, but not a deterministic CFL
- d)L3 is a deterministic CFL
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # i...
In formal language theory, a context-free language (CFL) is a language generated by some context-free grammar (CFG). Different CF grammars can generate the same CF language. It is important to distinguish properties of the language (intrinsic properties) from properties of a particular grammar (extrinsic properties). The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing. Indeed, given a CFG, there is a direct way to produce a pushdown automaton for the grammar (and corresponding language), though going the other way (producing a grammar given an automaton) is not as direct.
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Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # i...
Explanation:
L1={wwR∣w∈{0,1}∗}
- L1 is the language of all strings of the form wwR, where w is any string of 0s and 1s.
- L1 is a deterministic context-free language (DCFL) because it can be recognized by a deterministic pushdown automaton (PDA).
L2={w#wR∣w∈{0,1}∗}
- L2 is the language of all strings of the form w#wR, where w is any string of 0s and 1s.
- L2 is a deterministic context-free language (DCFL) because it can be recognized by a deterministic PDA.
L3={ww∣w∈(0,1}∗)
- L3 is the language of all strings of the form ww, where w is any non-empty string of 0s and 1s.
- L3 is a context-free language (CFL) because it can be recognized by a non-deterministic PDA.
- However, L3 is not a deterministic CFL because a deterministic PDA cannot handle the non-determinism involved in comparing two substrings of a string.
Therefore, the correct answer is option 'B', as L2 is a deterministic CFL.
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Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # is a special symbolL3={ww∣w∈(0,1}∗)Which one of the following is TRUE?a)L1 is a deterministic CFLb)L2 is a deterministic CFLc)L3 is a CFL, but not a deterministic CFLd)L3 is a deterministic CFLCorrect answer is option 'B'. Can you explain this answer?
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Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # is a special symbolL3={ww∣w∈(0,1}∗)Which one of the following is TRUE?a)L1 is a deterministic CFLb)L2 is a deterministic CFLc)L3 is a CFL, but not a deterministic CFLd)L3 is a deterministic CFLCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # is a special symbolL3={ww∣w∈(0,1}∗)Which one of the following is TRUE?a)L1 is a deterministic CFLb)L2 is a deterministic CFLc)L3 is a CFL, but not a deterministic CFLd)L3 is a deterministic CFLCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # is a special symbolL3={ww∣w∈(0,1}∗)Which one of the following is TRUE?a)L1 is a deterministic CFLb)L2 is a deterministic CFLc)L3 is a CFL, but not a deterministic CFLd)L3 is a deterministic CFLCorrect answer is option 'B'. Can you explain this answer?.
Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # is a special symbolL3={ww∣w∈(0,1}∗)Which one of the following is TRUE?a)L1 is a deterministic CFLb)L2 is a deterministic CFLc)L3 is a CFL, but not a deterministic CFLd)L3 is a deterministic CFLCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # is a special symbolL3={ww∣w∈(0,1}∗)Which one of the following is TRUE?a)L1 is a deterministic CFLb)L2 is a deterministic CFLc)L3 is a CFL, but not a deterministic CFLd)L3 is a deterministic CFLCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the languages L1={wwR∣w∈{0,1}∗}L2={w#wR∣w∈{0,1}∗}, where # is a special symbolL3={ww∣w∈(0,1}∗)Which one of the following is TRUE?a)L1 is a deterministic CFLb)L2 is a deterministic CFLc)L3 is a CFL, but not a deterministic CFLd)L3 is a deterministic CFLCorrect answer is option 'B'. Can you explain this answer?.
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