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:

There are 5 questions to complete.