1
GATE CSE 2003
+2
-0.6
Define Languages $${L_0}$$ and $${L_1}$$ as follows
$${L_0} = \left\{ { < M,\,w,\,0 > \left| {M\,\,} \right.} \right.$$ halts on $$\left. w \right\}$$
$${L_1} = \left\{ { < M,w,1 > \left| M \right.} \right.$$ does not halts on $$\left. w \right\}$$

Here $$< M,\,w,\,i >$$ is a triplet, whose first component, $$M$$ is an encoding of a Turing Machine, second component, $$w$$, is a string, and third component, $$t,$$ is a bit.
Let $$L = {L_0} \cup {L_1}.$$ Which of the following is true?

A
$$L$$ is recursively enumerable, but $$\overline L$$ is not
B
$$\overline L$$ is recursively enumerable, but $$L$$ is not
C
Both $$L$$ and $$\overline L$$ are recursive
D
Neither $$L$$ nor $$\overline L$$ is recursive enumerable
2
GATE CSE 2002
+2
-0.6
Which of the following is true?
A
The complement of a recursively language is recursive.
B
The complement of a recursively enumerable language is recursively enumerable.
C
The complement of a recursively language is either recursive or recursively enumerable.
D
The complement of a context-free language is context-free.
3
GATE CSE 2002
+2
-0.6
The $$C$$ language is:
A
A context free language
B
A context sensitive language
C
A regular language
D
Parsable fully only by a Turing machine
4
GATE CSE 1997
+2
-0.6
Which one of the following is not decidable?
A
Given a Turing machine $$M,$$ a stings s and an integer $$k,$$ $$M$$ accepts $$s$$ within $$k$$ steps
B
Equivalence of two given Turing machines
C
Language accepted by a given finite state machine is not empty
D
Language generated by a context free grammar is non empty
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
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