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 [ 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 s 0 , s 1 and s 2 where s 0 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. s 0 = input contains no vowels s 1 = Input contains exactly one vowel s 2 = input contains at least two vowels We then note that the state s 1 corresponds with inputs containing exactly one vowel, thus s 1 is the accepting state. If we are at state s 0 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 s 0 . If we are at state s 0 and the input is a vowel ( a, e, I, o, u ), then the input contains one vowel and thus we should move to state s 1 . If we are at state s 0 and the input is a consonant ( b, c, d, f, g, h, j, k, l

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Chapter 12.2, Problem 43ES

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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.

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Chapter 12.2, Problem 42ES

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Chapter 12 Solutions

Discrete Mathematics With Applications

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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.

Solution Summary: The author explains how to design a finite-state automaton to accept the language defined by the regular expression for all words that are written in lower-case letters.

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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.

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