Recursively enumerable sets and Turing machines

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Question 1

Which of the following statements is/are FALSE?

1. For every non-deterministic Turing machine, 
   there exists an equivalent deterministic Turing machine.
2. Turing recognizable languages are closed under union 
   and complementation.
3. Turing decidable languages are closed under intersection 
   and complementation.
4. Turing recognizable languages are closed under union 
   and intersection.

  • 1 and 4 only

  • 1 and 3 only

  • 2 only

  • 3 only

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Question 2

Let L1 be a recursive language. Let L2 and L3 be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?

  • L2 – L1 is recursively enumerable.

  • L1 – L3 is recursively enumerable

  • L2 ∩ L1 is recursively enumerable

  • L2 ∪ L1 is recursively enumerable

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Question 3

Let L1 be regular language, L2 be a deterministic context free language and L3 a recursively enumerable language, but not recursive. Which one of the following statements is false? , ISRO 2017

  • L3 ∩ L1 is recursive

  • L1 ∩ L2 ∩ L3 is recursively enumerable

  • L1 ∪ L2 is context free

  • L1 ∩ L2 is context free

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Question 4

Which of the following statements is/are TRUE?

  • Every subset of a recursively enumerable language is recursive.

  • If a language L and its complement L are both recursively enumerable, then L must be recursive.

  • The complement of a context-free language must be recursive

  • If L1 and L2 are regular, then L1∩ L2 must be deterministic context-free

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Question 5

Given the recursively enumerable language (LRE ), the context sensitive language (LCS ), the recursive language (LREC ), the context free language (LCF ) and deterministic context free language (LDCF ). The relationship between these families is given by

  • L CF ⊆ L DCF ⊆ LCS ⊆ LRE ⊆ LREC

  • L CF ⊆ L DCF ⊆ LCS ⊆ LREC ⊆ LRE

  • L DCF ⊆ L CF ⊆ LCS ⊆ LRE ⊆ LREC

  • L DCF ⊆ L CF ⊆ LCS ⊆ LREC ⊆ LRE

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Question 6

Given the following two statements: S1:If L1 and L2 are recursively enumerable languages over ∑, then L1 ∪ L 2 and L2 ∩ L2 are also recursively enumerable. S2: The set of recursively enumerable languages is countable. Which of the following is correct ?

  • S 1 is correct and S 2 is not correct

  • S 1 is not correct and S 2 is correct

  • Both S 1 and S 1 are not correct.

  • Both S 1 and S 1 are correct.

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Question 7

A problem whose language is recursive is called? , ISRO 2011

  • Unified problem

  • Boolean function

  • Recursive problem

  • Decidable

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Question 8

Which of the following is FALSE with respect to possible outcomes of executing a Turing Machine over a given input?

  • it may halt and accept the input

  • it may halt by changing the input

  • it may halt and reject the input

  • it may never halt

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Question 9

Which of the following pairs have different expressive power?
  • Single-tape-turing machine and multi-dimensional turing machine.
  • Multi-tape turing machine and multi-dimensional turing machine.
  • Deterministic push down automata and non-deterministic pushdown automata.
  • Deterministic finite automata and Non-deterministic finite automata
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Question 10

What is the highest type number that can be assigned to the following grammar? 

S → Aa
A → Ba
B → abc

  • Type 0

  • Type 1

  • Type 2

  • Type 3

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