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Convert this DFA to a regular expression using a GNFA. а, b b, d q2 а, с b, c а, d

Convert this DFA to a regular expression using a GNFA. а, b b, d q2 а, с b, c а, d

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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The image illustrates a Deterministic Finite Automaton (DFA) to be converted into a regular expression using a Generalized Nondeterministic Finite Automaton (GNFA). The DFA includes three states: \( q_1 \), \( q_2 \), and \( q_3 \). - **State \( q_1 \):** This is the start state, indicated by an incoming arrow without a source state. It has: - A self-loop with transitions on inputs 'a' and 'b'. - A transition to state \( q_2 \) on input 'a' and 'c'. - A transition to state \( q_3 \) on input 'c' and 'd'. - **State \( q_2 \):** - A self-loop with transitions on inputs 'b' and 'd'. - A transition to state \( q_3 \) on input 'b' and 'c'. - **State \( q_3 \):** - A transition back to state \( q_1 \) on inputs 'a' and 'd'. All states are represented by circles, and transitions are depicted as arrows labeled with the respective input symbols. Each state corresponds to a particular stage in the DFA, processing specific input characters according to the provided transitions. The goal is to convert the behavior of this DFA into a regular expression that describes the same language.
Transcribed Image Text:The image illustrates a Deterministic Finite Automaton (DFA) to be converted into a regular expression using a Generalized Nondeterministic Finite Automaton (GNFA). The DFA includes three states: \( q_1 \), \( q_2 \), and \( q_3 \). - **State \( q_1 \):** This is the start state, indicated by an incoming arrow without a source state. It has: - A self-loop with transitions on inputs 'a' and 'b'. - A transition to state \( q_2 \) on input 'a' and 'c'. - A transition to state \( q_3 \) on input 'c' and 'd'. - **State \( q_2 \):** - A self-loop with transitions on inputs 'b' and 'd'. - A transition to state \( q_3 \) on input 'b' and 'c'. - **State \( q_3 \):** - A transition back to state \( q_1 \) on inputs 'a' and 'd'. All states are represented by circles, and transitions are depicted as arrows labeled with the respective input symbols. Each state corresponds to a particular stage in the DFA, processing specific input characters according to the provided transitions. The goal is to convert the behavior of this DFA into a regular expression that describes the same language.
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