Computer science: Theory Of computation MCQs

6. Question

Consider two languages L1 and L2 each on the alphabet ∑. Let f: ∑ → X be a polynomial time computable bijection such that (∀x) [x ϵ  L , iff f(x) ϵ  L]. Further, let f1 be also polynomial time computable. Which of the following CANNOT be true?




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7. Question

A single tape Turing Machine M has two states q0 and q1. of which q0 is the starting state. The tape alphabet of M is {0, 1, B} and its input alphabet is {0,1}. The symbol B is the blank symbol used to indicate end of an input string. The transition function of M is described in the following table

0 1 B
q0 q1,1,R q1,1,R Halt
q1 q1,1,R q0,1,L q0,B,L

The table is interpreted as illustrated below. The entry (q1,1, R) in row q0 and column 1 signifies that if M is in state q0 and reads 1 on the current tape square, then it writes 1 on the same tape square, moves its tape head one position to the right and transitions to state q1

Which of the following statements is true about M?




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8. Question

Define languages L0 and L1 as follows:
L0 = {<M, w, 0> | M halts on w}
L1 = {<M, w, 1> | M does not halt on w}
Here <M, w, i> is a triplet, whose first component, M, is an encoding of a Turing
Machine, second component, w, is a string, and third component, i, is a bit.
Let L = L0ÈL1. Which of the following is true?




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9. Question

Consider the NFA M shown below.

Untitled

Let the language accepted by M be L. Let L1 be the language accepted by the NFA M1 obtained by changing the accepting state of M to a non-accepting state and by changing the non-accepting states of M to accepting states. Which of the following statements is true?




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10. Question

The problem 3-SAT and 2-SAT are




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