1
GATE CSE 2019
MCQ (Single Correct Answer)
+2
-0.67

Consider the following sets :

S1. Set of all recursively enumerable languages over the alphabet $\{0,1\}$

S2. Set of all syntactically valid C programs

S3. Set of all languages over the alphabet $\{0,1\}$

S4. Set of all non-regular languages over the alphabet $\{0,1\}$

Which of the above sets are uncountable?

A
S1 and S2
B
S3 and S4
C
S2 and S3
D
S1 and S4
2
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
The set of all recursively enumerable languages is
A
closed under complementation.
B
closed under intersection.
C
a subset of the set of all recursive languages
D
an uncountable set.
3
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
Consider the following problems. $$L(G)$$ denotes the language generated by a grammar $$G.$$ $$L(M)$$ denotes the language accepted by a machine $$M.$$

$$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ For an unrestricted grammar $$G$$ and a string $$W,$$ whether $$w \in L\left( G \right)$$
$$\,\,\,\,\,\,{\rm II}.\,\,\,\,\,\,\,$$ Given a Turing machine $$M,$$ whether $$L(M)$$ is regular
$$\,\,\,\,{\rm III}.\,\,\,\,\,\,\,$$ Given two grammars $${G_1}$$ and $${G_2}$$, whether $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)$$
$$\,\,\,\,{\rm IV}.\,\,\,\,\,\,\,$$ Given an $$NFA$$ $$N,$$ whether there is a deterministic $$PDA$$ $$P$$ such that $$N$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$\,\,\,\,\,\,\,\\,\,\,$$and $$P$$ accept the same language.

Which one of the following statements is correct?

A
Only $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ are undecidable
B
Only $${\rm III}$$ is undecidable
C
Only $${\rm I}$$$${\rm I}$$ and $${\rm IV}$$ are undecidable
D
Only $${\rm I}$$, $${\rm II}$$ and $${\rm III}$$ are undecidable
4
GATE CSE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$X$$ be a recursive language and $$Y$$ be a recursively enumerable but not recursive language. Let $$W$$ and $$Z$$ be two languages such that $$\overline Y $$ reduces to $$W,$$ and $$Z$$ reduces to $$\overline X $$ (reduction means the standard many-one reduction). Which one of the following statements is TRUE?
A
$$W$$ can be recursively enumerable and $$Z$$ is recursive.
B
$$W$$ can be recursive and $$Z$$ is recursively enumerable.
C
$$W$$ is not recursively enumerable and $$Z$$ is recursive.
D
$$W$$ is not recursively enumerable and $$Z$$ is not recursive.
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