Consider the NFA N₁ shown in Figure 1 over the alphabet Σ₁ = {0, 1}. 0 1 92 91 € X Figure 1: NFA N₁ for Problem 2. 0 0,1 93 1. What are the set of states, initial state, and accepting state(s) of the NFA N₁? 2. Write three elements in the the transition relation of N₁. 3. Explain in simple English what is the language recognized by N₁? 4. What is the compliment of the language recognized by N₁?

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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Consider the NFA \( N_1 \) shown in Figure 1 over the alphabet \( \Sigma_1 = \{0, 1\} \).

[Diagram: An NFA with three states \( q_1, q_2, q_3 \).]
- The initial state is \( q_1 \).
- Transition from \( q_1 \) to \( q_2 \) on input \( 1 \).
- Transition from \( q_1 \) to \( q_3 \) on input \( 0 \).
- Transition from \( q_3 \) to \( q_1 \) on \( \epsilon \) (epsilon transition).
- Transition from \( q_3 \) to \( q_2 \) on input \( 0 \) or \( 1 \).
- Accepting state is \( q_2 \).

*Figure 1: NFA \( N_1 \) for Problem 2.*

1. What are the set of states, initial state, and accepting state(s) of the NFA \( N_1 \)?

2. Write three elements in the transition relation of \( N_1 \).

3. Explain in simple English what is the language recognized by \( N_1 \)?

4. What is the complement of the language recognized by \( N_1 \)?
Transcribed Image Text:Consider the NFA \( N_1 \) shown in Figure 1 over the alphabet \( \Sigma_1 = \{0, 1\} \). [Diagram: An NFA with three states \( q_1, q_2, q_3 \).] - The initial state is \( q_1 \). - Transition from \( q_1 \) to \( q_2 \) on input \( 1 \). - Transition from \( q_1 \) to \( q_3 \) on input \( 0 \). - Transition from \( q_3 \) to \( q_1 \) on \( \epsilon \) (epsilon transition). - Transition from \( q_3 \) to \( q_2 \) on input \( 0 \) or \( 1 \). - Accepting state is \( q_2 \). *Figure 1: NFA \( N_1 \) for Problem 2.* 1. What are the set of states, initial state, and accepting state(s) of the NFA \( N_1 \)? 2. Write three elements in the transition relation of \( N_1 \). 3. Explain in simple English what is the language recognized by \( N_1 \)? 4. What is the complement of the language recognized by \( N_1 \)?
**Exercise 5:** 

Describe in simple English, the language represented by the following regular expressions.

(a) \((1 \cup 01 \cup 001)^*(\epsilon \cup 0 \cup 00)\)

(b) \((11 \cup 0)^*(00 \cup 1)^*\)

**Exercise 6:**

Prove that the concatenation operation is not commutative over regular languages (do not state that this result has been proved in class).
Transcribed Image Text:**Exercise 5:** Describe in simple English, the language represented by the following regular expressions. (a) \((1 \cup 01 \cup 001)^*(\epsilon \cup 0 \cup 00)\) (b) \((11 \cup 0)^*(00 \cup 1)^*\) **Exercise 6:** Prove that the concatenation operation is not commutative over regular languages (do not state that this result has been proved in class).
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In this question we will find elements and transition state and further prove concatenation operation is not commutative over regular expression.

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