1
GATE CSE 2014 Set 2
+1
-0.3
Let $$A\,\,{ \le _m}\,\,B$$ denotes that language $$A$$ is mapping reducible (also known as many-to-one reducible) to language $$B.$$ Which one of the following is FALSE?
A
If $$A\,\,{ \le _m}\,\,B$$ and $$B$$ is recursive then $$A$$ is recursive.
B
If $$A\,\,{ \le _m}\,\,B$$ and $$A$$ is undecidable then $$B$$ is un-decidable.
C
If $$A\,\,{ \le _m}\,\,B$$ and $$B$$ is recursively enumerable then $$A$$ is recursively enumerable.
D
If $$A\,\,{ \le _m}\,\,B$$ and $$B$$ is not recursively enumerable then $$A$$ is not recursively enumerable.
2
GATE CSE 2013
+1
-0.3
Which of the following statements is/are FALSE?
$$1.$$ For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine
$$2.$$ Turing recognizable languages are closed under union and complementation
$$3.$$ Turing decidable languages are closed under intersection and complementation
$$4.$$ Turing recognizable languages are closed under union and intersection
A
$$1$$ and $$4$$ only
B
$$1$$ and $$3$$ only
C
$$2$$ only
D
$$3$$ only
3
GATE CSE 2008
+1
-0.3
Which of the following is true for the language $$\left\{ {{a^p}} \right.\left| P \right.$$ prime $$\left. \, \right\}$$?
A
It is not accepted by a Turing machine
B
It is regular but not context-free
C
It is context-free but not regular
D
It is neither regular nor context-free, but accepted by a Turing machine
4
GATE CSE 2003
+1
-0.3
Nobody knows yet if $$P=NP$$. Consider the language $$L$$ defined as follows
$$L = \left\{ {\matrix{ {{{\left( {0 + 1} \right)}^ * }\,\,\,if\,\,P = NP} \cr {\,\,\,\,\,\,\,\phi \,\,\,\,Otherwise} \cr } } \right.$$

Which of the following statement is true?

A
$$L$$ is recursive
B
$$L$$ is recursively enumerable but not recursive
C
$$L$$ is not recursively enumerable
D
Whether $$L$$ is recursive or not will be known after we find out if $$P=NP.$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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