Question 3

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

Question 5

Let be the encoding of a Turing machine as a string over ∑= {0, 1}. Let L = { |M is a Turing machine that accepts a string of length 2014 }. Then, L is

Question 7

Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable. Which one of the following is TRUE?

Question 8

Consider two languages L1 and L2 each on the alphabet ∑. Let f : ∑ → ∑ be a polynomial time computable bijection such that (∀ x) [x ∈ L1 if f(x) ∈ L2]. Further, let f^{-1} be also polynomial time computable. Which of the following CANNOT be true?

Question 9

Consider the following problem X.

Given a Turing machine M over the input alphabet Σ, any state q of M And a word w∈Σ*, does the computation of M on w visit the state q?Which of the following statements about X is correct?

Question 10

Consider the following decision problems:

(P1) Does a given finite state machine accept a given string (P2) Does a given context free grammar generate an infinite number of strings

Which of the following statements is true?

There are 27 questions to complete.

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