2,5,451,6,7.8,2 NFA

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
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Convert NFA to DFA

### Explanation of NFA Diagram

This image represents a Non-deterministic Finite Automaton (NFA) diagram, which is a conceptual machine used in computer science to recognize patterns or process strings of input based on defined rules.

#### Components:
1. **States**: The circles labeled with letters (A, S, C, T, E) represent the states of the NFA. 
   - **State A**: Start state, indicated with an arrow pointing towards it.
   - **State E**: Accepting or final state, indicated with a double circle.

2. **Transitions**: The arrows between the states indicate possible transitions and are labeled with the conditions for those transitions.
   - From **A to S**: On input 0-9.
   - From **S to B**: On input 0-9.
   - Loop at **S**: On input 0-9.
   - From **B to C**: On input λ (lambda), representing an epsilon transition (without input).
   - From **C to T**: Series of transitions on input 0, then dot (.), then 0.
   - Loop at **T**: On input 0.
   - From **T to E**: On input 0, 1, 2, 9.
   - Loop at **E**: On input 0, 1, 2, 9.

#### Inputs:
- The initial input set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

### How It Works:
- The NFA starts at state A and processes the input string.
- If the input character matches the condition (number 0-9), it transitions to the corresponding state.
- Epsilon transitions (as indicated by λ) allow the automaton to change states without consuming an input character.
- The goal is to reach the accepting state E after consuming the input string, following valid transitions as per the NFA diagram. 

This NFA is designed to recognize specific numeric patterns defined by the transitions among its states.
Transcribed Image Text:### Explanation of NFA Diagram This image represents a Non-deterministic Finite Automaton (NFA) diagram, which is a conceptual machine used in computer science to recognize patterns or process strings of input based on defined rules. #### Components: 1. **States**: The circles labeled with letters (A, S, C, T, E) represent the states of the NFA. - **State A**: Start state, indicated with an arrow pointing towards it. - **State E**: Accepting or final state, indicated with a double circle. 2. **Transitions**: The arrows between the states indicate possible transitions and are labeled with the conditions for those transitions. - From **A to S**: On input 0-9. - From **S to B**: On input 0-9. - Loop at **S**: On input 0-9. - From **B to C**: On input λ (lambda), representing an epsilon transition (without input). - From **C to T**: Series of transitions on input 0, then dot (.), then 0. - Loop at **T**: On input 0. - From **T to E**: On input 0, 1, 2, 9. - Loop at **E**: On input 0, 1, 2, 9. #### Inputs: - The initial input set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. ### How It Works: - The NFA starts at state A and processes the input string. - If the input character matches the condition (number 0-9), it transitions to the corresponding state. - Epsilon transitions (as indicated by λ) allow the automaton to change states without consuming an input character. - The goal is to reach the accepting state E after consuming the input string, following valid transitions as per the NFA diagram. This NFA is designed to recognize specific numeric patterns defined by the transitions among its states.
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DFA of the given epsilon NFA

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