# Finite State Machine (FSM) Diagram Analysis## Diagram Description:The FSM diagram consists of four states: q0, q1, q2, and q3. The diagram illustrates transitions between these states based on input symbols 'a' or 'b'. The initial state is q0, indicated by an arrow pointing towards it from the left.- **q0:** - Transition to q1 on input 'a'. - Transition to itself on input 'b'.- **q1:** - Transition to q2 on input 'a'. - Transition to q0 on input 'b'.- **q2:** - Transition to q3 on input 'b'. - Transition to itself on input 'a'.- **q3:** (Accepting state) - Transition to itself on input 'a' or 'b'.## Problem Statement:Identify the correct description of the language accepted by the FSM M from the following options:1. \( L(M) = \{ w \in \{a, b\}^* : w \text{ contains the substring } ab \} \).2. \( L(M) = \{ w \in \{a, b\}^* : w \text{ does not contain the substring } ab \} \).3. \( L(M) = \{ w \in \{a, b\}^* : w \text{ does not contain the substring } aab \} \).4. \( L(M) = \{ w \in \{a, b\}^* : w \text{ contains the substring } aab \} \).## Explanation:To determine the language accepted by FSM M, analyze the transition path to the accepting state q3. The FSM reaches q3 only when the specific substring "aab" is encountered. Therefore, the correct description of the language accepted by the FSM is:- \( L(M) = \{ w \in \{a, b\}^* : w \text{ contains the substring } aab \} \).This corresponds to Option 4.

Finite state machine (FSM) is replication of a model that is used to compute over the states to work…

Given the following FSM M, the correct statements are: فه 90 q1 q2 _ L(M) = {w € {a, b}* : w contains the substring ab}. □ L(M) = {w € {a, b}* : w does not contain the substring ab}. _ L(M) = {w € {a, b}* : w does not contain the substring aab]. _ L(M) = {w € {a, b}* : w contains the substring aab}. 93

Given the following FSM M, the correct statements are: فه 90 q1 q2 _ L(M) = {w € {a, b}* : w contains the substring ab}. □ L(M) = {w € {a, b}* : w does not contain the substring ab}. _ L(M) = {w € {a, b}* : w does not contain the substring aab]. _ L(M) = {w € {a, b}* : w contains the substring aab}. 93

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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# Finite State Machine (FSM) Diagram Analysis

## Diagram Description:
The FSM diagram consists of four states: q0, q1, q2, and q3. The diagram illustrates transitions between these states based on input symbols 'a' or 'b'. The initial state is q0, indicated by an arrow pointing towards it from the left.

- **q0:**
- Transition to q1 on input 'a'.
- Transition to itself on input 'b'.

- **q1:**
- Transition to q2 on input 'a'.
- Transition to q0 on input 'b'.

- **q2:**
- Transition to q3 on input 'b'.
- Transition to itself on input 'a'.

- **q3:** (Accepting state)
- Transition to itself on input 'a' or 'b'.

## Problem Statement:
Identify the correct description of the language accepted by the FSM M from the following options:

1. \( L(M) = \{ w \in \{a, b\}^* : w \text{ contains the substring } ab \} \).
2. \( L(M) = \{ w \in \{a, b\}^* : w \text{ does not contain the substring } ab \} \).
3. \( L(M) = \{ w \in \{a, b\}^* : w \text{ does not contain the substring } aab \} \).
4. \( L(M) = \{ w \in \{a, b\}^* : w \text{ contains the substring } aab \} \).

## Explanation:
To determine the language accepted by FSM M, analyze the transition path to the accepting state q3. The FSM reaches q3 only when the specific substring "aab" is encountered. Therefore, the correct description of the language accepted by the FSM is:

- \( L(M) = \{ w \in \{a, b\}^* : w \text{ contains the substring } aab \} \).

This corresponds to Option 4.

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