Consider the language L given by (assume Σ = { 2 } )
L = {2^nk | k > 0, and n is non − negative integer number}
The minimum number of states of finite automaton which accept the language L is

Question

Question

This question was previously asked in

UGC NET Computer Science (Paper 2) Dec 2018 Paper

Attempt in App

Answer 1

Given language is : L = {2^nk | k > 0, and n is non − negative integer number}

Case 1:

Consider n = 1,

Then k can be 1, 2 ,3,….

Strings possible in this case : {2, 2², 2³, 2⁴,…………}

DFA for this:

States possible with n = 1 are 2.

Case 2:

When n = 2

Then k can be 1, 2, 3….

Strings possible in this case : {2², 2⁴, 2⁶, 2⁸,……}

DFA for this:

States possible when n = 2 are 3.

So, in general we are getting n + 1 states in DFA