Let a digit be one of the ten decimal digits 0,1,2,3,4,5,6,7,8,9. Draw the state diagram for a DFA that recognizes the language of digit strings that represent base-10 numbers that are one more than a multiple of three. For example, your DFA should accept 07658 since 07654=7654= 3(2551) + 1. On the other hand, 7655 would not be accepted since 7655= 3(2551) + 2. Hint: Use three states, representing numbers of the form 3n, 3n+1 and 3n+2. Think about what happens when we add a digit to the end of a given number. For example, when we add a 0, 3n+1, for example, will go to 10 (3n+1) = 3(10n+3)+1, in other words, back to a number of the form 3n+1. The same thing will happen when we add a 3, 6 or 9 to the end. Continuing in this way you can fill in all the transitions between the three states. Upload a pic of your state diagram.
Let a digit be one of the ten decimal digits 0,1,2,3,4,5,6,7,8,9. Draw the state diagram for a DFA that recognizes the language of digit strings that represent base-10 numbers that are one more than a multiple of three. For example, your DFA should accept 07658 since 07654=7654= 3(2551) + 1. On the other hand, 7655 would not be accepted since 7655= 3(2551) + 2. Hint: Use three states, representing numbers of the form 3n, 3n+1 and 3n+2. Think about what happens when we add a digit to the end of a given number. For example, when we add a 0, 3n+1, for example, will go to 10 (3n+1) = 3(10n+3)+1, in other words, back to a number of the form 3n+1. The same thing will happen when we add a 3, 6 or 9 to the end. Continuing in this way you can fill in all the transitions between the three states. Upload a pic of your state diagram.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Let a digit be one of the ten decimal digits 0,1,2,3,4,5,6,7,8,9. Draw the state diagram for a DFA that recognizes the language of digit strings
that represent base-10 numbers that are one more than a multiple of three. For example, your DFA should accept 07658 since 07654 = 7654 = 3(2551) + 1.
On the other hand, 7655 would not be accepted since 7655= 3(2551) + 2.
Hint: Use three states, representing numbers of the form 3n, 3n+1 and 3n+2. Think about what happens when we add a digit to the end of a given number.
For example, when we add a 0, 3n+1, for example, will go to 10(3n+1) = 3(10n+3)+1, in other words, back to a number of the form 3n+1. The same thing will
happen when we add a 3, 6 or 9 to the end. Continuing in this way you can fill in all the transitions between the three states.
Upload a pic of your state diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6a64cc1-e6e9-4ab0-9555-433f302860a0%2Fa1fb8bd0-74f0-4fbb-931c-d533a1f393f2%2Fg55hkwn_processed.png&w=3840&q=75)
Transcribed Image Text:Let a digit be one of the ten decimal digits 0,1,2,3,4,5,6,7,8,9. Draw the state diagram for a DFA that recognizes the language of digit strings
that represent base-10 numbers that are one more than a multiple of three. For example, your DFA should accept 07658 since 07654 = 7654 = 3(2551) + 1.
On the other hand, 7655 would not be accepted since 7655= 3(2551) + 2.
Hint: Use three states, representing numbers of the form 3n, 3n+1 and 3n+2. Think about what happens when we add a digit to the end of a given number.
For example, when we add a 0, 3n+1, for example, will go to 10(3n+1) = 3(10n+3)+1, in other words, back to a number of the form 3n+1. The same thing will
happen when we add a 3, 6 or 9 to the end. Continuing in this way you can fill in all the transitions between the three states.
Upload a pic of your state diagram.
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