# Theory Of Computation MCQ - Context free languages

6:

P, Q, R are three languages, if P and R are regular and if PQ = R, then

 A. Q has to be regular B. Q cannot be regular C. Q need not be regular D. Q cannot be a CFL Option: C Explanation :
7:

A class of language that is closed under

 A. union and complementation has to be closed under intersection B. intersection and complement has to be closed under union C. union and intersection has to be closed under complementation D. both (A) and (B) Option: D Explanation :
8:

The productions
E—>E+E
E—>E—E
E-->E*E
E —> E / E
E —> id

 A. generate an inherently ambiguous language B. generate an ambiguous language but not inherently so C. are unambiguous D. can generate all possible fixed length valid computation for carrying out addition, subtraction, multipication and division, which can be expressed in one expression Option: B Explanation :
9:

Which of the folowing definitions below generates the same language as L, where
L = {xn yn such that n > = 1} ?

I. E —> xEy | xy

II. xy | (x+ xyy+)

III .x+y+

 A. I only B. I and II C. II and III D. II only Option: A Explanation : II generates strings like xxyyy, which are not supposed to be. III generates strings like xyy, which are not supposed to be. I can be verified to generate all the strings in L and only those.
10:

Following context free grammar
S —> aB | bA
A —>b | aS | bAA
B —> b | bS | aBB

generates strings of terminals that have

 A. equal number of a's and b's B. odd number of a's and odd number b's C. even number of a's and even number of b's D. odd number of a's and even number of a's Option: A Explanation : S —> aB —> aaBB-->aabB —> aabb So (b) is wrong. We have S --> a B —> a b So (c) is wrong. A careful observation of the productions will reveal a similarity. Change A to B, B to A, a to b and b to a. The new set of productions will be the same as the original set. So (d) is false and (a) is the correct answer.

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Syllabus covered in this section is-

• Regular languages and finite automata
• Context free languages and Push-down automata
• Recursively enumerable sets and Turing machines
• Undecidability, NPcompleteness
• Models of computation-Finite Automata
• Pushdown Automata
• Non-detenninism and NFA. DPDA and PDAs and Languages accepted by these Structures
• Grammars, Languages,
• Non- computability and Examples of non-computable problems

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