1
GATE CSE 2022
MCQ (Single Correct Answer)
+1
-0.33

Which one of the following regular expressions correctly represents the language of the finite automation given below?

GATE CSE 2022 Theory of Computation - Finite Automata and Regular Language Question 2 English

A
ab*bab* + ba*aba*
B
(ab*b)* ab* + (ba*a)*ba*
C
(ab*b + ba*a)* (a* + b*)
D
(ba*a + ab*b)* (ab* + ba*)
2
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Which of the following statements is/are TRUE?

A
Every subset of a recursively enumerable language is recursive.
B
If a language L and its complement $$\overline L $$ are both recursively enumerable, then L must be recursive.
C
Complement of a context-free language must be recursive.
D
If L1 and L2 are regular, then L1 $$\cap$$ L2 must be deterministic context-free.
3
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Which of the following is/are undecidable?

A
Given two Turing machines M1 and M2, decide if L(M1) = L(M2).
B
Given a Turing machine M, decide if L(M) is regular.
C
Given a Turing machine M, decide if M accepts all strings.
D
Given a Turing machine M, decide if M takes more than 1073 steps on every string.
4
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Consider the following languages:

L1 = {an wan | w $$\in$$ {a, b}*}

L2 = {wxwR | w, x $$\in$$ {a, b}*, | w | , | x | > 0}

Note that wR is the reversal of the string w. Which of the following is/are TRUE?

A
L1 and L2 are regular.
B
L1 and L2 are context-free
C
L1 is regular and L2 is context-free.
D
L1 and L2 are context-free but not regular.
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