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2) Minimize the following DFAS: a 2 a b b b a 2 3 (3 a 3 a b a a a,b b a 5 5 a 6

2) Minimize the following DFAS: a 2 a b b b a 2 3 (3 a 3 a b a a a,b b a 5 5 a 6

Database System Concepts
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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--- ## Homework Assignments 1-4 ### 2) Minimize the following DFAs: #### DFA 1: - **States**: 1, 2, 3, 4, 5 - **Alphabet**: {a, b} - **Transitions**: - From state 1: - 'a' to state 2 - 'b' to state 3 - From state 2: - 'a' to state 1 - 'b' to state 4 - From state 3: - 'a' to state 5 - 'b' to state 1 - From state 4: - 'a' to state 5 - 'b' to state 5 - From state 5: - 'a' to state 4 - 'b' to state 5 - **Accepting States**: 4, 5 #### DFA 2: - **States**: 1, 2, 3, 4, 5, 6 - **Alphabet**: {a, b} - **Transitions**: - From state 1: - 'a' to state 2 - 'b' to state 3 - From state 2: - 'a' to state 1 - 'b' to state 4 - From state 3: - 'a' to state 4 - 'b' to state 5 - From state 4: - 'a' to state 6 - 'b' to state 5 - From state 5: - 'a' to state 6 - 'b' to state 3 - From state 6: - 'a' to state 6 - 'b' to state 5 - **Accepting States**: All states ### 3) When dealing with strings, exponents denote repetition. For example: - \(a^2 = aa\) - \(a^3 = aaa\) - \(a^n = n \, \text{a's}\) Construct a DFA over the alphabet {a, b} that recognizes the language of all words ending in \(a^xb^
Transcribed Image Text:--- ## Homework Assignments 1-4 ### 2) Minimize the following DFAs: #### DFA 1: - **States**: 1, 2, 3, 4, 5 - **Alphabet**: {a, b} - **Transitions**: - From state 1: - 'a' to state 2 - 'b' to state 3 - From state 2: - 'a' to state 1 - 'b' to state 4 - From state 3: - 'a' to state 5 - 'b' to state 1 - From state 4: - 'a' to state 5 - 'b' to state 5 - From state 5: - 'a' to state 4 - 'b' to state 5 - **Accepting States**: 4, 5 #### DFA 2: - **States**: 1, 2, 3, 4, 5, 6 - **Alphabet**: {a, b} - **Transitions**: - From state 1: - 'a' to state 2 - 'b' to state 3 - From state 2: - 'a' to state 1 - 'b' to state 4 - From state 3: - 'a' to state 4 - 'b' to state 5 - From state 4: - 'a' to state 6 - 'b' to state 5 - From state 5: - 'a' to state 6 - 'b' to state 3 - From state 6: - 'a' to state 6 - 'b' to state 5 - **Accepting States**: All states ### 3) When dealing with strings, exponents denote repetition. For example: - \(a^2 = aa\) - \(a^3 = aaa\) - \(a^n = n \, \text{a's}\) Construct a DFA over the alphabet {a, b} that recognizes the language of all words ending in \(a^xb^
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