Recursively enumerable sets and Turing machines

Question 21

If L and P are two recursively enumerable languages, then they are not closed under

• Kleene Star L * of L
• Intersection L ∩ P
• Union L ∪ P
• Set Difference

Question 22

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

Question 23

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

Question 24

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

Question 25

A problem whose language is recursive is called?

• Unified problem
• Boolean function
• Recursive problem
• Decidable

Question 26

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.

Question 27

Given the recursively enumerable language (L_RE ), the context sensitive language (L_CS ), the recursive language (L_REC ), the context free language (L_CF ) and deterministic context free language (L_DCF ). The relationship between these families is given by

• L _CF ⊆ L _DCF ⊆ L_CS ⊆ L_RE ⊆ L_REC

• L _CF ⊆ L _DCF ⊆ L_CS ⊆ L_REC ⊆ L_RE

• L _DCF ⊆ L _CF ⊆ L_CS ⊆ L_RE ⊆ L_REC

• L _DCF ⊆ L _CF ⊆ L_CS ⊆ L_REC ⊆ L_RE

Question 28

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?

• L3 ∩ L1 is recursive
• L1 ∩ L2 ∩ L3 is recursively enumerable
• L1 ∪ L2 is context free
• L1 ∩ L2 is context free

Question 29

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