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Discrete Mathematics With ApplicationsConsider again the finite-state automaton of exercise 3. a. To what state does the automaton go when the symbols of the following strings are input to it in sequence, starting from the initial state? (i) bb (ii) aabbbaba (iii) babbbbbabaa (iv) bbaaaabaa b. Which of the strings in part (a) send the automaton to an accepting state? c. What is the language accepted by the automaton? d. Find a regular expression that defines the language.BuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 12.2, Problem 13ES

Textbook Problem

Consider again the finite-state automaton of exercise 3.

a. To what state does the automaton go when the symbols of the following strings are input to it in sequence, starting from the initial state?

(i) *bb *(ii) *aabbbaba *(iii) *babbbbbabaa *(iv) *bbaaaabaa *b. Which of the strings in part (a) send the automaton to an accepting state?

c. What is the language accepted by the automaton?

d. Find a regular expression that defines the language.

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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