   Chapter 12.2, Problem 44ES ### 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
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# 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. 44. Exercise 36

To determine

The finite-state automaton to return the words that start with a consonant and contains exactly two consecutive vowels.

Explanation

Given information:

The first letter of the word should not be a vowel and if there is a vowel in the word the next letter also should be a vowel (exactly two vowels)

Let x be a set such that x={x|vowelsinuppercaseletters} and y be a set such that y={y|consonantsinuppercaseletters}.

Now we can define a I, the set of inputs as I={x,y}.

Let the initial state be s0. For the input x, s0 does not response. Hence, automaton keeps its state on s0 because the first letter should be a consonant.

When we input y to the initial state, s0 is satisfied and move onto the next state s1 such that s1 is the state, the first letter is selected

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