This set of Automata Theory Multiple Choice Questions & Answers (MCQs) focuses on “Extended Transition Function”.

1. The number of tuples in an extended Non Deterministic Finite Automaton:

a) 5

b) 6

c) 7

d) 4

View Answer

Explanation: For NFA or extended transition function on NFA, the tuple elements remains same i.e. 5.

2. Choose the correct option for the given statement:

Statement: The DFA shown represents all strings which has 1 at second last position.

a) Correct

b) Incorrect, Incomplete DFA

c) Wrong proposition

d) May be correct

View Answer

Explanation: The given figure is an NFA. The statement contradicts itself.

3. What is wrong in the given definition?

Def: ({q0, q1, q2}, {0,1}, δ, q3, {q3})

a) The definition does not satisfy 5 Tuple definition of NFA

b) There are no transition definition

c) Initial and Final states do not belong to the Graph

d) Initial and final states can’t be same

View Answer

Explanation: q3 does not belong to Q where Q= set of finite states.

4. If δ is the transition function for a given NFA, then we define the δ’ for the DFA accepting the same language would be:

Note: S is a subset of Q and a is a symbol.

a) δ’ (S, a) =U_{pϵs} δ (p, a)

b) δ’ (S, a) =U_{p≠s} δ (p, a)

c) δ’ (S, a) =U_{pϵs} δ(p)

d) δ’ (S) =U_{p≠s} δ(p)

View Answer

Explanation: According to subset construction, equation 1 holds true.

5. What is the relation between DFA and NFA on the basis of computational power?

a) DFA > NFA

b) NFA > DFA

c) Equal

d) Can’t be said

View Answer

Explanation: DFA is said to be a specific case of NFA and for every NFA that exists for a given language, an equivalent DFA also exists.

6. If a string S is accepted by a finite state automaton, S=s_{1}s_{2}s_{3}……s_{n} where s_{i}ϵ∑ and there exists a sequence of states r0, r1, r2…… rn such that δ(r(i), s_{i+1}) =r_{i+1} for each 0, 1, …n-1, then r(n) is:

a) initial state

b) transition symbol

c) accepting state

d) intermediate state

View Answer

Explanation: r(n) is the final state and accepts the string S after the string being traversed through r(i) other states where I ϵ 01,2…(n-2).

7. According to the given table, compute the number of transitions with 1 as its symbol but not 0:

a) 4

b) 3

c) 2

d) 1

View Answer

Explanation: The transition graph is made and thus the answer can be found.

8. From the given table, δ*(q0, 011) =?

a) {q0}

b) {q1} U {q0, q1, q2}

c) {q2, q1}

d) {q3, q1, q2, q0}

View Answer

Explanation: δ*(q0,011) = U

_{rϵ}δ*(q0,01) δ (r, 1) = {q0, q1, q2}.

9. Number of times the state q3 or q2 is being a part of extended 6 transition state is

a) 6

b) 5

c) 4

d) 7

View Answer

Explanation: According to the question, presence of q2 or q1 would count so it does and the answer according to the diagram is 6.

10. Predict the missing procedure:

1.Δ(Q0, ε) ={Q0},

2.Δ(Q0, 01) = {Q0, Q1}

3.δ(Q0, 010) =?

a) {Q0, Q1, Q2}

b) {Q0, Q1}

c) {Q0, Q2}

d) {Q1, Q2}

View Answer

Explanation: According to given table and extended transition state implementation, we can find the state at which it rests.

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