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?
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?
S1 and S2 | |
S3 and S4 | |
S2 and S3 | |
S1 and S4 |
Question 1 Explanation:
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)?
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)?
I and IV only | |
II and III only | |
II, III and IV only | |
III and IV only |
Question 2 Explanation:
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?
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?
I and IV only | |
II and III only | |
III and IV only | |
II and IV only |
Question 3 Explanation:
Question 4 |
Which one of the following problems is undecidable?
Deciding if a given context-free grammar is ambiguous | |
Deciding if a given string is generated by a given context-free grammar | |
Deciding if the language generated by a given context-free grammar is empty | |
Deciding if the language generated by a given context-free grammar is finite. |
Question 4 Explanation:
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?
Both 2^{\Sigma^{*}} and \Sigma^{*} are countable | |
2^{\Sigma^{*}} is countable \Sigma^{*} is uncountable | |
2^{\Sigma^{*}} is uncountable and \Sigma^{*} is countable | |
Both 2^{\Sigma^{*}} and \Sigma^{*} are uncountable |
Question 5 Explanation:
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?
If A\leq _{m}B and B is recursive then A is recursive | |
If A\leq _{m}B and A is undecidable then B is undecidable | |
If A\leq _{m}B and B is recursively enumerable then A is recursively enumerable. | |
If A\leq _{m}B and B is not recursively enumerable then A is not recursively enumerable |
Question 6 Explanation:
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)?
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)?
3 only | |
3 and 4 only | |
1, 2 and 3 only | |
2 and 3 only |
Question 7 Explanation:
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?
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?
1, 2, 3, 4 | |
1,2 | |
2,3,4 | |
3,4 |
Question 8 Explanation:
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
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
I and II | |
I and IV | |
II and III | |
II and IV |
Question 9 Explanation:
Question 10 |
Which of the following problems is undecidable?
Membership problem for CFGs. | |
Ambiguity problem for CFGs. | |
Finiteness problem for FSAs. | |
Equivalence problem for FSAs. |
Question 10 Explanation:
There are 10 questions to complete.