Write the o function for the following transition graphs (1) dfa (Sp5a : Q ×£→ Q) ak a 91 92 (2) nfa (SNF4 : Q × (EU{2}) → P(Q)) a, b a

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
icon
Related questions
Question
**Transcription for Educational Website**

**1. Write the δ function for the following transition graphs:**

**(1) DFA (δ<sub>DFA</sub> : Q × Σ → Q)**

- **State Diagram:**
  - The DFA consists of three states: \(q_0\), \(q_1\), and \(q_2\).
  - Start state: \(q_0\).
  - Accepting state: \(q_1\).
  - Transitions:
    - From \(q_0\): 
      - On input 'a', transition to \(q_1\).
      - On input 'b', transition to \(q_2\).
    - From \(q_1\): 
      - On input 'a' or 'b', loop back to \(q_1\) (self-loop).
    - From \(q_2\):
      - On input 'a' or 'b', loop back to \(q_2\) (self-loop).

**(2) NFA (δ<sub>NFA</sub> : Q × (Σ ∪ {λ}) → P(Q))**

- **State Diagram:**
  - The NFA consists of three states: \(q_0\), \(q_1\), and \(q_2\).
  - Start state: \(q_0\).
  - Accepting state: \(q_1\).
  - Transitions:
    - From \(q_0\): 
      - On input 'a', transition to \(q_1\).
      - On input 'b', transition to \(q_2\).
    - From \(q_1\): 
      - On input 'a' or 'b', self-loop (stay at \(q_1\)).
      - On λ (epsilon transition), move to \(q_2\).
    - From \(q_2\):
      - On input 'b', transition back to \(q_0\).

**2. Give the languages accepted in the above (1) and (2), respectively.**

- Explanation of languages:
  - For the DFA, describe the language based on the transition rules.
  - For the NFA, discuss the significance of epsilon transitions in the language acceptance.

This transcription provides a detailed explanation of the transition graphs for both a DFA and an NFA, useful for students learning about
Transcribed Image Text:**Transcription for Educational Website** **1. Write the δ function for the following transition graphs:** **(1) DFA (δ<sub>DFA</sub> : Q × Σ → Q)** - **State Diagram:** - The DFA consists of three states: \(q_0\), \(q_1\), and \(q_2\). - Start state: \(q_0\). - Accepting state: \(q_1\). - Transitions: - From \(q_0\): - On input 'a', transition to \(q_1\). - On input 'b', transition to \(q_2\). - From \(q_1\): - On input 'a' or 'b', loop back to \(q_1\) (self-loop). - From \(q_2\): - On input 'a' or 'b', loop back to \(q_2\) (self-loop). **(2) NFA (δ<sub>NFA</sub> : Q × (Σ ∪ {λ}) → P(Q))** - **State Diagram:** - The NFA consists of three states: \(q_0\), \(q_1\), and \(q_2\). - Start state: \(q_0\). - Accepting state: \(q_1\). - Transitions: - From \(q_0\): - On input 'a', transition to \(q_1\). - On input 'b', transition to \(q_2\). - From \(q_1\): - On input 'a' or 'b', self-loop (stay at \(q_1\)). - On λ (epsilon transition), move to \(q_2\). - From \(q_2\): - On input 'b', transition back to \(q_0\). **2. Give the languages accepted in the above (1) and (2), respectively.** - Explanation of languages: - For the DFA, describe the language based on the transition rules. - For the NFA, discuss the significance of epsilon transitions in the language acceptance. This transcription provides a detailed explanation of the transition graphs for both a DFA and an NFA, useful for students learning about
Expert Solution
Step 1- Transition function for given DFA

Transition function for DFA is:

δ:Q*εQ

where Q= Finite set of states

ε= input alphabet

The transitions for the given DFA are:

δ:{q0}*{a}{q1}δ:{q0}*{b}{q2}δ:{q1}*{a}{q1}δ:{q1}*{b}{q1}δ:{q2}*{a}{q2}δ:{q2}*{b}{q2}

 

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education