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Test: Turing Machine: RE, REC & Undecidability- 1


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10 Questions MCQ Test Question Bank for GATE Computer Science Engineering | Test: Turing Machine: RE, REC & Undecidability- 1

Test: Turing Machine: RE, REC & Undecidability- 1 for Computer Science Engineering (CSE) 2022 is part of Question Bank for GATE Computer Science Engineering preparation. The Test: Turing Machine: RE, REC & Undecidability- 1 questions and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus.The Test: Turing Machine: RE, REC & Undecidability- 1 MCQs are made for Computer Science Engineering (CSE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Turing Machine: RE, REC & Undecidability- 1 below.
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Test: Turing Machine: RE, REC & Undecidability- 1 - Question 1

Which of the following functions are computable with Turning Machine?

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 1

All the above functions are total recursive functions. The total recursive functions are like recursive language. Turing machine halts on each and every input of recursive language. All of the above functions are turing computable.

Test: Turing Machine: RE, REC & Undecidability- 1 - Question 2

A countable union of countable sets is not

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 2

A countable union of countable set is countable. Countably infinite and denumerable are alternate names of countable sets.

Test: Turing Machine: RE, REC & Undecidability- 1 - Question 3

∑* over {0,1} and 2∑* are respectively,

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 3

Since ∑* is all the combinations of 0 and 1 and yet it is enumerable and belongs to the category of countably infinite. But 2∑* is the power set of ∑* which is infinite. By diagonalisation theorem, power set of any countably infinite set is always uncountable, hence 2∑*​ belongs to uncountably infinite set.

Test: Turing Machine: RE, REC & Undecidability- 1 - Question 4

Which of the following is undecidable?

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 4

According to the decision properties of the CFL and Regular languages, Equivalence of regular languages and emptiness of regular languages are decidable. Also the finiteness of CFL is decidable. For each of above property an algorithm exist. But no algorithm exist for checking the equivalence of the two context-free language.

Test: Turing Machine: RE, REC & Undecidability- 1 - Question 5

The statement "ATM can’t solve halting problem’’ is

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 5

ATM cannot solves the halting problem because it cannot find in finite time that for the given word the machine will halt or not.

Test: Turing Machine: RE, REC & Undecidability- 1 - Question 6

A PDA behaves like a TM when the number of auxiliary memory it has, is

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 6

Auxiliary memory = memory used by the machine for calculations or swappings.
PDA with 2 or more stacks is equivalent to TM.

Test: Turing Machine: RE, REC & Undecidability- 1 - Question 7

Halting problem/language is

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 7

Halting problem belongs to the TM. The language in which halting problem belongs is recursively enumerable i.e. RE. In this TM can’t tell in finite time the word is rejected or not. Although it can tell in finite time that the given word is accepted or not. Although REC can tell in finite time and comes into halt about both i.e.

Test: Turing Machine: RE, REC & Undecidability- 1 - Question 8

The statement is

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 8

The statement   is always true.

Test: Turing Machine: RE, REC & Undecidability- 1 - Question 9

If e1 and e2 are the RE denoting the languages Land L2 respectively, then which of the following is wrong?

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 9

Choice (c) is wrong since “φ” is a regular. In fact  

*Multiple options can be correct
Test: Turing Machine: RE, REC & Undecidability- 1 - Question 10

Which of the following is in P?
PATH, HAMPATH, SAT, 3SAT

Detailed Solution for Test: Turing Machine: RE, REC & Undecidability- 1 - Question 10

SAT and PATH is in P while 3SAT and HAMPATH are NPC.

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