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onvert this DFA to a regular expression using a GNFA. а, d c, d q1 q2 93 а, b а, d ъ, с c, b

onvert this DFA to a regular expression using a GNFA. а, d c, d q1 q2 93 а, b а, d ъ, с c, b

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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Convert this DFA to a regular expression using a GNFA.

**Converting a DFA to a Regular Expression Using a GNFA** To convert a Deterministic Finite Automaton (DFA) to a regular expression using a Generalized Nondeterministic Finite Automaton (GNFA), one can follow an algorithmic approach that incrementally simplifies the DFA by eliminating states and updating the transitions accordingly. Below, we have a detailed explanation of the DFA provided and the step-by-step process for conversion. ### Diagram Description: 1. **States**: - **q1** (initial and accepting state) - **q2** - **q3** 2. **Transitions**: - From **q1** to **q1** with inputs **a, d**. - From **q1** to **q2** with inputs **a, b**. - From **q2** to **q2** with inputs **a, d**. - From **q2** to **q1** with inputs **b, c**. - From **q2** to **q3** with inputs **c, d**. - From **q3** to **q3** with inputs **b, c**. ### Steps to Convert DFA to Regular Expression: 1. **Add Start and Final States**: Add a new start state **qs** with epsilon (ε) transitions to the initial state **q1** and add a new final state **qf**. Connect every existing final state to **qf** with epsilon (ε) transitions. 2. **Remove States One by One**: - In each step, remove an intermediate state and update the transitions between the remaining states with new regular expressions that account for the routes through the removed state. 3. **Generalize Transition Labels**: Replace the transition between states with generalized regular expressions that combine existing paths. 4. **Simplify the Expression**: Once only **qs** and **qf** remain, the regular expression representing the language accepted by the original DFA will be on the edge from **qs** to **qf**. ### Key Steps Involved: **Initial Configuration**: - Start state `qs` transitions to `q1` with ε. - Accept state `q1` transitions to `qf` with ε. **Intermediate Steps**: - Remove state `q2`: - Update the transitions using the paths that go
Transcribed Image Text:**Converting a DFA to a Regular Expression Using a GNFA** To convert a Deterministic Finite Automaton (DFA) to a regular expression using a Generalized Nondeterministic Finite Automaton (GNFA), one can follow an algorithmic approach that incrementally simplifies the DFA by eliminating states and updating the transitions accordingly. Below, we have a detailed explanation of the DFA provided and the step-by-step process for conversion. ### Diagram Description: 1. **States**: - **q1** (initial and accepting state) - **q2** - **q3** 2. **Transitions**: - From **q1** to **q1** with inputs **a, d**. - From **q1** to **q2** with inputs **a, b**. - From **q2** to **q2** with inputs **a, d**. - From **q2** to **q1** with inputs **b, c**. - From **q2** to **q3** with inputs **c, d**. - From **q3** to **q3** with inputs **b, c**. ### Steps to Convert DFA to Regular Expression: 1. **Add Start and Final States**: Add a new start state **qs** with epsilon (ε) transitions to the initial state **q1** and add a new final state **qf**. Connect every existing final state to **qf** with epsilon (ε) transitions. 2. **Remove States One by One**: - In each step, remove an intermediate state and update the transitions between the remaining states with new regular expressions that account for the routes through the removed state. 3. **Generalize Transition Labels**: Replace the transition between states with generalized regular expressions that combine existing paths. 4. **Simplify the Expression**: Once only **qs** and **qf** remain, the regular expression representing the language accepted by the original DFA will be on the edge from **qs** to **qf**. ### Key Steps Involved: **Initial Configuration**: - Start state `qs` transitions to `q1` with ε. - Accept state `q1` transitions to `qf` with ε. **Intermediate Steps**: - Remove state `q2`: - Update the transitions using the paths that go
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