Table of Contents

1 TOC Questions for GATE Exam Practice

TOC Questions for GATE Exam Practice

Some important theory of computation tutorial questions and toc gate questions for practice for the gate exam cse aspirants. Here toc gate questions from different topic in automata theory such as dfa questions ,and regular expression questions in automata has been covered in this practice set.

Computer science students are advised to practice and learn theory of computation tutorial as per syllabus of gate cse syllabus 2021 before attempt these

Questions and Answers

A computer science graduate should have the knowledge about following questions and answer or the concepts in order to attempt these toc gate questions.

Concepts of DFA
Concepts of NFA
Regular Expression in automata.
What is Context Free Language ?
What is Grammar in theory of automata ?

Note – Don’t forget to study Views in SQL

Theory of Computation Tutorial for GATE

Here in this theory of computation tutorial we have discussed some previous year toc gate questions with their answer.

Q1. Consider S and T be languages over ={a,b} and these are represented by the given regular expressions (a+b*)* and (a+b)*, respectively. Then find the correct statement among the following (GATE CS 2000)

(a) S is a subset of

(b) T is a subset of S

(d) S ∩T=Ø

Answer: (c).

2.A language L denotes the language generated by the grammar S – OSO/00. Then find the correct statement? (GATE CS 2000)

(a) L = O⁺

(b) L is regular but not O⁺

(d) L is not context free

Answer: (b)

3.Consider the following two statements:

S1: { 0^2n |n >= l} is a regular language
S2: { 0^m 0^n 0^(m+n) l m >= 1 and n >= 2} is a regular language

Which is true ? (GATE CS 2001)

a) Only S1 is correct
b) Only S2 is correct
c) Both S1 and S2 are correct
d) None of S1 and S2 is correct.

Answer: (c)

Find the correct statement among the following? (GATE CS 2001)

(a) If a language is context free it can always be accepted by a deterministic push-down automaton

(b) The union of two context free languages is context free

(d) The complement of a context free language is context free

Answer: (b)

TOC Questions for GATE Exam Practice

Here in this sections we have discussed some toc questions for gate exam practice with their solution and answer.

1. Number of trivial substrings in “GATE2013” are:

(a) 37 (b) 35

2. Let the string be defined over symbols a and b then what will be the number of states in minimal DFA, if every string starts and ends with different symbols?

(a) 5 (b) 4

3. The total number of substrings present in “GATE” is:

(a) 7 (b) 10

4. Let Σ= {a, b}, what are the number of states in minimal DFA, length of every string congruent

to mod 5.

(a) 2 (b) 3

5. A minimal DFA that is equivalent to a NDFA has:

A. Always more states (b) Always less no. of states

C. Exactly 2n states (d) Sometimes more states

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6. Consider following Regular Expression:

(i) a*b*b (a+ (ab)*)* b*

(ii) a*(ab + ba)* b*

Find the length of shortest string which is in both (i) & (ii)?

(a) 2 (b) 3

7. S àAB

Aà BB/ a

Bà AB/ b

Choose incorrect statement?

A. aabbb can be derived from above grammar

B. aabb can be derived from above grammar

C. ababab can be derived from above grammar

D. abbb can be derived from above grammar

8. One of the following Regular Expressions is not the same as others. Which one?

(a) (a* + b*a*)* (b) (a*b* + b*a*)* (a*b*)*

9. The complement of CFL:

(a) Recursive (b) Recursive enumerated

10. The language of primes in unary is:

(a) Regular (b) CFL

11. Consider the regular grammar generating the set of all strings ending with ‘00’, with terminals {0,1} and non-terminals {S, A, B}, S being the initial state and B, the final state.

S–> 1/ 0 →0

→0/1/0

The production missing is

(a) →1 (b) →

12. What are the number of states needed in minimal DFA, that accepts (1+1111)*, with 1 as alphabet here.

(a) 5 (b) 4

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13. Consider the grammar:

SàaSbS/ bSaS/ ε,

Which one among the following is the smallest which has twp deviation trees.?

(a) abab (b) aabb

14. The language L= { aNbN/ 0< N < 327th Prime number} is

(a) Regular (b) Not context sensitive

15. Consider the set of input Σ= {a},

And assume language, L= {a2012.K/ K> 0},

Which among the following is the value of minimum number of states that is needed in a DFA to recognize the given language L?

(a) 22012 + 1 (b) 2013

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16. The following CFG,

Sà aB/ bA

Aà a/ aS/ bAA

Bà b/ bS/ aBB generates strings with

(a) Odd number of a’s & odd number of b’s

(b) Even number of a’s & even number of b’s

(d) Odd number of a’s & even number of b’s

17. What type of grammar is this most accurately described as?

Sàb/aD

Dà a/aDD

(a) A regular grammar (b) CFG

18. Consider the following NFA M over the alphabet {0,1}.

Let M1 be the NFA obtained by interchanging final and non-final states of M. Let the language accepted by M be L and that accepted by M1 be L1. Choose correct statement:

(a) L1= L (b) L1∩ L2= Φ

19. Let M= (Q, Σ, δ, S, F) and M’= (Q, Σ, δ, S, Q – F) where M accepts L and M’ accepts L1 and M is NFA, which among the following is the relation between L and L’ ?

(a) L and L’ are complement to each other

(b) L and L’ are similar to each other

(d) None of the above

Answer Sheet and Explanation

The answers and explanation of the solution for the questions as discussed in above theory of computation tutorial are given below

Solution: Option (c)

Explanation:

For any string, there will always be only 2 trivial substrings, ∈ and the given string itself.

2.Solution: Option (a)

3.Solution (c)

4.Solution: Option (c)

5.Solution: Option (d)

6.Solution: Option (d)

Explanation: The shortest string is generated by both the regular expressions

Solution: Option (b)
Solution: Option (c)

Explanation: abb cannot be generated by C, whereas it is generated by all other regular expressions.

Solution: Option (a)

Solution: Option (d)

Explanation:

The language of primes in unary is {1/ }. Finite automata cannot recognize this language as it has no memory. Push Down Automata also cannot recognize this because there is no pattern in the strings that can be remembered using one stack. LBA can accept this, so it is a context sensitive language.