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This question contains multiple parts. You must answer all parts completely to be successful at this skill. A The pumping length of the following deterministic finite automata is 4 because there are four states. 0

This question contains multiple parts. You must answer all parts completely to be successful at this skill. A The pumping length of the following deterministic finite automata is 4 because there are four states. 0

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
Problem 1PE
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**Skill 6, Attempt 2** This question contains multiple parts. You must answer all parts completely to be successful at this skill. **A** The pumping length of the following deterministic finite automata is 4 because there are four states. ### State Diagram Explanation The state diagram consists of four states: \( Q_0, Q_1, Q_2, \) and \( Q_3 \). - **\( Q_0 \)**: This is the start state, represented by an arrow pointing to it from nowhere. It has a loop back to itself on input 0 and transitions to \( Q_1 \) on input 1. The transition to \( Q_3 \) occurs on input 0 or 1. - **\( Q_1 \)**: From \( Q_1 \), the automaton transitions to \( Q_2 \) on input 1 and returns to \( Q_0 \) on input 0. - **\( Q_2 \)**: Moves to \( Q_3 \) on input 1 and loops back to itself on input 0 in the path from \( Q_3 \). - **\( Q_3 \)**: \( Q_3 \) is an accepting state, indicated by a double circle. It transitions back to itself on input 0 and transitions to \( Q_2 \) on input 1. ### Answer the following: 1. State a string of length 4 or greater that is accepted by the deterministic finite automaton. 2. Decompose the string into the \( x, y, \) and \( z \) substrings so that the conclusions of the pumping lemma hold. 3. Highlight a loop in the state diagram that corresponds to the substring \( y \).
Transcribed Image Text:**Skill 6, Attempt 2** This question contains multiple parts. You must answer all parts completely to be successful at this skill. **A** The pumping length of the following deterministic finite automata is 4 because there are four states. ### State Diagram Explanation The state diagram consists of four states: \( Q_0, Q_1, Q_2, \) and \( Q_3 \). - **\( Q_0 \)**: This is the start state, represented by an arrow pointing to it from nowhere. It has a loop back to itself on input 0 and transitions to \( Q_1 \) on input 1. The transition to \( Q_3 \) occurs on input 0 or 1. - **\( Q_1 \)**: From \( Q_1 \), the automaton transitions to \( Q_2 \) on input 1 and returns to \( Q_0 \) on input 0. - **\( Q_2 \)**: Moves to \( Q_3 \) on input 1 and loops back to itself on input 0 in the path from \( Q_3 \). - **\( Q_3 \)**: \( Q_3 \) is an accepting state, indicated by a double circle. It transitions back to itself on input 0 and transitions to \( Q_2 \) on input 1. ### Answer the following: 1. State a string of length 4 or greater that is accepted by the deterministic finite automaton. 2. Decompose the string into the \( x, y, \) and \( z \) substrings so that the conclusions of the pumping lemma hold. 3. Highlight a loop in the state diagram that corresponds to the substring \( y \).
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