Undecidability

Question 1
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
GATE CSE 2019      Undecidability
Question 2
Let L(R) be the language represented by regular expression R. Let L(G) be the language generated by a context free grammar G. Let L (M) be the language accepted by a Turning machine M. Which of the following decision problems are undecidable ?

I. Given a regular expression R and a string w, is w\in L(R)?
II. Given a context-free grammar G, L(G)=\phi?
III. Given a context-free grammar G, is L(G)=\Sigma* for some alphabet \Sigma?
IV. Given a Turning machine M and a string w, is w\inL(M)?
A
I and IV only
B
II and III only
C
II, III and IV only
D
III and IV only
GATE CSE 2017 SET-2      Undecidability
Question 3
Which of the following decision problems are undecidable?
I. Given NFAs N1 and N2, is L(N1)\capL(N2) = \phi?
II. Given a CFG G = (N,\Sigma ,P,S) and a string x \in\Sigma ^*, does x \in L(G)?
III. Given CFGs G1 and G2, is L(G1) = L(G2)?
IV. Given a TM M, is L(M) = \phi?
A
I and IV only
B
II and III only
C
III and IV only
D
II and IV only
GATE CSE 2016 SET-1      Undecidability
Question 4
Which one of the following problems is undecidable?
A
Deciding if a given context-free grammar is ambiguous
B
Deciding if a given string is generated by a given context-free grammar
C
Deciding if the language generated by a given context-free grammar is empty
D
Deciding if the language generated by a given context-free grammar is finite.
GATE CSE 2014 SET-3      Undecidability
Question 5
Let \Sigma be a finite non-empty alphabet and let 2^{\Sigma^{*}} be the power set of \Sigma^{*} . Which one of the following is TRUE?
A
Both 2^{\Sigma^{*}} and \Sigma^{*} are countable
B
2^{\Sigma^{*}} is countable \Sigma^{*} is uncountable
C
2^{\Sigma^{*}} is uncountable and \Sigma^{*} is countable
D
Both 2^{\Sigma^{*}} and \Sigma^{*} are uncountable
GATE CSE 2014 SET-3      Undecidability
Question 6
Let A \leq _{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\leq _{m}B and B is recursive then A is recursive
B
If A\leq _{m}B and A is undecidable then B is undecidable
C
If A\leq _{m}B and B is recursively enumerable then A is recursively enumerable.
D
If A\leq _{m}B and B is not recursively enumerable then A is not recursively enumerable
GATE CSE 2014 SET-2      Undecidability
Question 7
Which of the following is/are undecidable?
1. G is a CFG. Is L(G) = \Phi?
2. G is a CFG. Is L(G) = \Sigma ^{*} ?
3. M is a Turing machine. Is L(M) regular?
4. A is a DFA and N is an NFA. Is L(A) = L(N)?
A
3 only
B
3 and 4 only
C
1, 2 and 3 only
D
2 and 3 only
GATE CSE 2013      Undecidability
Question 8
Which of the following problems are decidable?
1) Does a given program ever produce an output?
2) If L is a context-free language, then, is \bar{L} also context-free?
3) If L is a regular language, then, is \bar{L} also regular?
4) If L is a recursive language, then, is \bar{L} also recursive?
A
1, 2, 3, 4
B
1,2
C
2,3,4
D
3,4
GATE CSE 2012      Undecidability
Question 9
Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free
A
I and II
B
I and IV
C
II and III
D
II and IV
GATE CSE 2008      Undecidability
Question 10
Which of the following problems is undecidable?
A
Membership problem for CFGs.
B
Ambiguity problem for CFGs.
C
Finiteness problem for FSAs.
D
Equivalence problem for FSAs.
GATE CSE 2007      Undecidability
There are 10 questions to complete.

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