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Discrete Mathematics With ApplicationsA simplified telephone switching system allows the following strings as legal telephone numbers: a. A string of seven digits in which neither of the first two digits is a 0 or 1 (a local call string). b. A 1 followed by a three-digit area code string (any digit except 0 or I followed by a 0 or I followed by any digit) followed by a seven- digit local call string. c. A 0 alone or followed by a three-digit area code string plus a seven-digit local call string. Design a finite-state automaton to recognize all the legal telephone numbers in (a), (b), and (c). Include an “error state” for invalid telep hone numbers.BuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 12.2, Problem 48ES

Textbook Problem

A simplified telephone switching system allows the following strings as legal telephone numbers:

a. A string of seven digits in which neither of the first two digits is a 0 or 1 *(a local call string). *b. A 1 followed by a three-digit

c. A 0 alone or followed by a three-digit area code string plus a seven-digit local call string.

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

Discrete Mathematics With Applications

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Ch. 12.1 - If x and y are strings, the concatenation of x and...Ch. 12.1 - If L and Lare languages, the Concatenation of L...Ch. 12.1 - If L and Lare languages, the union of L and L is...Ch. 12.1 - If L is a language, the Kleene closure of L is...Ch. 12.1 - The set of regular expressions over an alphabet is...Ch. 12.1 - The function that associates a language to each...Ch. 12.1 - The notation [A-C] is an example of a____ and...Ch. 12.1 - Use of a single dot in a regular expression stands...Ch. 12.1 - The symbol ^, placed at the beginning of a...Ch. 12.1 - If r is a regular expression, the notation r +...

Ch. 12.1 - If r is a regular expression, the notation...Ch. 12.1 - If r is a regular expression, the notation r{n}...Ch. 12.1 - In 1 and 2, let={x,y} be an alphabet. 1. a. Let...Ch. 12.1 - In 1 and 2, let={x,y} be an alphabet. 2. a. Let L3...Ch. 12.1 - If the expression ab+cd+ in postfix notation is...Ch. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - In 25—27, find a regular expression that defines...Ch. 12.1 - In 25—27, find a regular expression that defines...Ch. 12.1 - In 25—27, find a regular expression that defines...Ch. 12.1 - Let r, s, and t be regular expressions over...Ch. 12.1 - Let r, s, and t be regular expressions over...Ch. 12.1 - Let r, s, and t be regular expressions over...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - Write a regular expression to perform a complete...Ch. 12.1 - Write a regular expression to define the set of...Ch. 12.2 - The five objects that make up a finite-state...Ch. 12.2 - The next-state table for an automaton shows the...Ch. 12.2 - In the annotated next-state table, the initial...Ch. 12.2 - A string w consisting of input symbols is accepted...Ch. 12.2 - The language accepted by a finite-state automaton...Ch. 12.2 - If N is the next-stale function for a finite-state...Ch. 12.2 - One part of Kleene’s theorem says that given any...Ch. 12.2 - The second part of Kleene’s theorem says that...Ch. 12.2 - A regular language is .__________Ch. 12.2 - Given the language consisting of all strings of...Ch. 12.2 - Find the state of the vending machine in Example...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 8 and 9, a finite-state automaton is given by...Ch. 12.2 - In 8 and 9, a finite-state automaton is given by...Ch. 12.2 - A finite-state automaton A given by the transition...Ch. 12.2 - A finite-state automaton A given by the transition...Ch. 12.2 - Consider again the finite-state automaton of...Ch. 12.2 - Consider again the finite-state automaton of...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - A simplified telephone switching system allows the...Ch. 12.2 - Write a computer algorithm that simulates the...Ch. 12.2 - Write a computer algorithm that simulates the act...Ch. 12.2 - Let L be the language consisting of all strings of...Ch. 12.2 - Let L be the language consisting of all strings of...Ch. 12.2 - Let L be the language consisting of all strings of...Ch. 12.2 - a. Let A be a finite-state automaton with input...Ch. 12.3 - Given a finite-state automaton A with...Ch. 12.3 - Given a finite-state automaton A with...Ch. 12.3 - Given states s and t in a finite-state automaton...Ch. 12.3 - If A is a finite-state automaton, then for some...Ch. 12.3 - Given a finite-state automaton A, the set of...Ch. 12.3 - Consider the finite-state automaton A given by the...Ch. 12.3 - Consider the finite-state automaton A given by the...Ch. 12.3 - Consider the finite-state automaon A discussed in...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Are the automata A and A’ shown below equivalent?Ch. 12.3 - Are the automata A and A’ shown below equivalent?Ch. 12.3 - Are the automata A and A’ shown below equivalent?Ch. 12.3 - Are the automata A and A’ shown below equivalent?Ch. 12.3 - Prove property (12.3.1).Ch. 12.3 - How should the proof of property (12.3.1) be...Ch. 12.3 - Prove property (12.3.3).Ch. 12.3 - Prove property (12.3.4).Ch. 12.3 - Prove property (12.3.5).Ch. 12.3 - Prove property (12.3.6).Ch. 12.3 - Prove that if two states of a finite-state...Ch. 12.3 - Write a complete proof of property (12.3.7).

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