In 29—47, design a finite-state automaton to accept the language defined by the regular expression in the referenced exercise from Section 12.1.

43. Exercise 35

To design a finite-state automaton to accept the languagedefined by the regular expression for all the words that are written in lower case letters contain exactly one of the vowels a, e, i, o, or u.

Given information:

All words that are written in lower-case letters and containexactly one of the vowels a, e, i, o, or u.

Calculation:

Given:

All words in lower-case letters containing exactly one vowel.

Let [a−z] represent all lower-case letters.

The vowels are e, u, i, o and u

The constants are b, c, d, f, g, h, j, k, l. m, n, p, q, r, s, t, v, w, x, y, z.

Let us design an automaton with 3 states s0,s1 and s2 where s0 is the initial state. We draw each of the states as a circle with the name of the state within the circle. We draw an arrow towards the initial state and draw a second circle within the accepting states.

s0= input contains no vowelss1= Input contains exactly one vowels2= input contains at least two vowels

We then note that the state s₁ corresponds with inputs containing exactly one vowel, thus s₁ is the accepting state.

If we are at state s₀ and the input is a consonant ( b, c, d, f, g, h, j, k, l. m, n, p, q, r, s, t, v, w, x, y, z ), then the input still contains no vowels and thus we should remain at state s₀.

If we are at state s₀ and the input is a vowel ( a, e, I, o, u ), then the input contains one vowel and thus we should move to state s₁.

If we are at state s₀ and the input is a consonant ( b, c, d, f, g, h, j, k, l