   Chapter 12.2, Problem 43ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# 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 determine

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.

Explanation

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 [az] 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

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 