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State Reduction, Regular Expressions and CFL 1. Use the state reduction algorithm we talked in class to simplify and reduce the DFA below. What strings does it accept? Simply state a rule (no need to prove it). 6 9 a 10 94

State Reduction, Regular Expressions and CFL 1. Use the state reduction algorithm we talked in class to simplify and reduce the DFA below. What strings does it accept? Simply state a rule (no need to prove it). 6 9 a 10 94

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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**State Reduction, Regular Expressions, and CFL** 1. **Task**: Use the state reduction algorithm we discussed in class to simplify and reduce the DFA given below. What strings does it accept? Simply state a rule (no need to prove it). **Diagram Explanation**: The diagram is a directed graph representing a Deterministic Finite Automaton (DFA) with six states. The nodes are labeled as \(q1\), \(q2\), \(q3\), \(q4\), \(q5\), and \(q6\). - **Initial State**: \(q1\) (indicated by an arrow pointing to it). - **Transitions**: - \(q1 \to q2\) on input \(a\). - \(q1 \to q6\) on input \(b\). - \(q2 \to q5\) on input \(a\). - \(q2 \to q3\) on input \(b\). - \(q3 \to q5\) on input \(a\). - \(q4 \to q3\) on input \(a\). - \(q4 \to q6\) on input \(b\). - \(q5 \to q5\) on input \(a\). - \(q5 \to q4\) on input \(b\). - \(q6 \to q3\) on input \(b\). - **Accepting State**: \(q5\) (indicated by a double circle). This DFA illustrates various state transitions based on inputs 'a' and 'b', which determine the acceptance or rejection of strings by reaching the accepting state \(q5\).
Transcribed Image Text:**State Reduction, Regular Expressions, and CFL** 1. **Task**: Use the state reduction algorithm we discussed in class to simplify and reduce the DFA given below. What strings does it accept? Simply state a rule (no need to prove it). **Diagram Explanation**: The diagram is a directed graph representing a Deterministic Finite Automaton (DFA) with six states. The nodes are labeled as \(q1\), \(q2\), \(q3\), \(q4\), \(q5\), and \(q6\). - **Initial State**: \(q1\) (indicated by an arrow pointing to it). - **Transitions**: - \(q1 \to q2\) on input \(a\). - \(q1 \to q6\) on input \(b\). - \(q2 \to q5\) on input \(a\). - \(q2 \to q3\) on input \(b\). - \(q3 \to q5\) on input \(a\). - \(q4 \to q3\) on input \(a\). - \(q4 \to q6\) on input \(b\). - \(q5 \to q5\) on input \(a\). - \(q5 \to q4\) on input \(b\). - \(q6 \to q3\) on input \(b\). - **Accepting State**: \(q5\) (indicated by a double circle). This DFA illustrates various state transitions based on inputs 'a' and 'b', which determine the acceptance or rejection of strings by reaching the accepting state \(q5\).
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