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(1) Given the description of L1 and L2 as regular in the form of acceptors M1 and M2. Show that the following languages are regular by constructing an automaton using generic descriptions of M below: M fowo (i) L1U L2 (ii) L1 L2 (iii) Li complement

(1) Given the description of L1 and L2 as regular in the form of acceptors M1 and M2. Show that the following languages are regular by constructing an automaton using generic descriptions of M below: M fowo (i) L1U L2 (ii) L1 L2 (iii) Li complement

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
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Hi everyone, I need help with automata, please

 

### Problem Statement: Given the description of \( L_1 \) and \( L_2 \) as regular languages in the form of acceptors \( M_1 \) and \( M_2 \). Show that the following languages are regular by constructing an automaton using generic descriptions of \( M \) below: ![Diagram of a generic automaton \( M \) consisting of a start state leading to a series of transitions, ending in an accepting state.] ### Tasks: (i) Demonstrate that \( L_1 \cup L_2 \) is regular. (ii) Demonstrate that \( L_1 L_2 \) (concatenation) is regular. (iii) Demonstrate that the complement of \( L_1 \) is regular. ### Explanation of Diagram: The diagram is a generic representation of a finite automaton \( M \). It begins with a start state, represented by a circle with an arrow pointing to it. This state leads to a succession of states highlighted by lines with wave-like transitions and ends in a double-circle, indicating an accepting state. This generic sketch serves as a foundation for constructing specific automata that satisfy the conditions of regular languages \( L_1 \cup L_2 \), \( L_1L_2 \), and the complement of \( L_1 \).
Transcribed Image Text:### Problem Statement: Given the description of \( L_1 \) and \( L_2 \) as regular languages in the form of acceptors \( M_1 \) and \( M_2 \). Show that the following languages are regular by constructing an automaton using generic descriptions of \( M \) below: ![Diagram of a generic automaton \( M \) consisting of a start state leading to a series of transitions, ending in an accepting state.] ### Tasks: (i) Demonstrate that \( L_1 \cup L_2 \) is regular. (ii) Demonstrate that \( L_1 L_2 \) (concatenation) is regular. (iii) Demonstrate that the complement of \( L_1 \) is regular. ### Explanation of Diagram: The diagram is a generic representation of a finite automaton \( M \). It begins with a start state, represented by a circle with an arrow pointing to it. This state leads to a succession of states highlighted by lines with wave-like transitions and ends in a double-circle, indicating an accepting state. This generic sketch serves as a foundation for constructing specific automata that satisfy the conditions of regular languages \( L_1 \cup L_2 \), \( L_1L_2 \), and the complement of \( L_1 \).
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