Explanation Given information: A simplified telephone switching system allows the following strings as legal telephone numbers: A string of seven digits in which neither of the first two digits is a 0 or 1 (a local call string). A 1 followed by a 3-digit area code string (any digit except 0 or 1 followed by a 0 or 1 followed by any digit) followed by a seven-digit local call string. A 0 alone or followed by a three-digit area code string plus a seven-digit local call string. Calculation: By the given information, we design an automaton with 11 states s 0 , s 1 , s 2 , ... , s 10 where s 0 is the initial state. Let [ 0 − 9 ] represent all digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 and let [ 2 − 9 ] represent the digits 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 . s 0 = No input or a 0/1 followed by a 0 or 1, followed by a digit that is not 0 nor 1, followed by a 0 or 1, followed by a digit. s 1 = Input is a 0 or 1. s 2 = Input is a 0 or 1, followed by a digit that is neither 0 nor 1, followed by a 0 or 1. s 3 = Input is a 0 or 1, followed by a digit that is neither 0 nor 1, followed by a 0 or 1. s 4 = Input is the string until the first digit in the local call string. s 5 = Input is the string until the second digit in the local call string. s 6 = Input is the string until the third digit in the local call string. s 7 = Input is the string until the fourth digit in the local call string. s 8 = Input is the string until the fifth digit in the local call string. s 9 = Input is the string until the sixth digit in the local call string. s 10 = Input is the string until the seventh digit in the local call string. s 11 = Remaining inputs. If we are at state s 0 and the input is 0 or 1, then we move to state s 1 . If we are at state s 0 and the input is another digit, then the input represents the first digit in the local call string and thus we move to state s 3 . If we are at state s 1 and the input is 0 or 1, then we obtain an invalid telephone number and thus we move to state s 11

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ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 12.2, Problem 48ES

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A finite-state automaton to recognize all the legal telephone numbers in (a), (b) and (c) and to include an “error state” for invalid telephone numbers.

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Chapter 12.2, Problem 47ES

Chapter 12.2, Problem 49ES

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To design: A finite-state automaton to recognize all the legal telephone numbers in (a), (b) and (c) and to include an “error state” for invalid telephone numbers.

Solution Summary: The author explains how to design a finite-state automaton to recognize all the legal telephone numbers in (a), (b) and (c).

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To design: A finite-state automaton to recognize all the legal telephone numbers in (a), (b) and (c) and to include an “error state” for invalid telephone numbers.

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Chapter 12 Solutions

To design:

A finite-state automaton to recognize all the legal telephone numbers in (a), (b) and (c) and to include an “error state” for invalid telephone numbers.