DESIGN OF A FINITE STATE MACHINE || Formal Languages Automata Theory

Consider the finite state, machine with the following characteristics:

Set of states: Q = {q₀, q₁, q₂, q₃}

ALPHABET: Where the input string comes from ∑ = {a, b}

INITIAL STATE: Where the start head starts at first element q₀ = {q₀}

SET OF CAPITAL/ACCEPT STATE: if we stop there we accept the input the input F = {q₀, q₁, q₂}   

TRANSITION FUNCTION δ: Rules how to form state. The following are the transition rules:

From state q₀ and with input a, go to state q₀

δ (q_0, a) = q₀

From state q₀ and with input b, go to state q₁

δ (q_0, b) = q₁

From state q₁ and with input a, go to state q₂

δ (q_1, a) = q₀

From state q₁ and with input b, go to state q₀

δ (q_1, a) = q₂

From state q₂ and with input a, go to state q₀

δ (q_2, a) = q₀

From state q₂ and with input b, go to state q₀

δ (q_2, b) = q₂

From state q₃ and with any input go to state q₃

                                                            δ (q_3, a) = q₃ (or) δ (q_3, b) = q₃

The transitions are given in the following table and diagram.

Transition table:

Inputs States	Parent inputs
	A	b
è  *q0	q0	q1
*q1	q0	q2
*q2	q0	q3
q3	q3	q3