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Removing state q1, find a PDA with three states that accepts the same language as the PDA in Example 7.2. (Page 14 in the chapter 7's slide).

Removing state q1, find a PDA with three states that accepts the same language as the PDA in Example 7.2. (Page 14 in the chapter 7's slide).

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Removing state \( q_1 \), find a PDA with three states that accepts the same language as the PDA in Example 7.2. (Page 14 in the chapter 7's slide).
Transcribed Image Text:Removing state \( q_1 \), find a PDA with three states that accepts the same language as the PDA in Example 7.2. (Page 14 in the chapter 7's slide).
### Example 7.2: Consider the NPDA The NPDA (Nondeterministic Pushdown Automaton) is defined as follows: - **States (Q):** \(\{ q_0, q_1, q_2, q_3 \}\) - **Input Alphabet (Σ):** \(\{ a, b \}\) - **Stack Alphabet (Γ):** \(\{ 0, 1 \}\) - **Initial Stack Symbol (z):** 0 - **Final States (F):** \(\{ q_3 \}\) The initial state is \(q_0\), and the transition function is defined by: - \(\delta(q_0, a, 0) = \{ (q_1, 10), (q_3, \lambda) \}\) - \(\delta(q_0, \lambda, 0) = \{ (q_3, \lambda) \}\) - \(\delta(q_1, a, 1) = \{ (q_1, 11) \}\) - \(\delta(q_1, b, 1) = \{ (q_2, \lambda) \}\) - \(\delta(q_2, b, 1) = \{ (q_2, \lambda) \}\) - \(\delta(q_2, \lambda, 0) = \{ (q_3, \lambda) \}\) These transitions describe how the NPDA moves between states and manipulates the stack based on the input symbols and current stack contents. The machine uses nondeterminism, allowing for multiple possible transitions at each step. The goal is to reach a final state with an empty input string.
Transcribed Image Text:### Example 7.2: Consider the NPDA The NPDA (Nondeterministic Pushdown Automaton) is defined as follows: - **States (Q):** \(\{ q_0, q_1, q_2, q_3 \}\) - **Input Alphabet (Σ):** \(\{ a, b \}\) - **Stack Alphabet (Γ):** \(\{ 0, 1 \}\) - **Initial Stack Symbol (z):** 0 - **Final States (F):** \(\{ q_3 \}\) The initial state is \(q_0\), and the transition function is defined by: - \(\delta(q_0, a, 0) = \{ (q_1, 10), (q_3, \lambda) \}\) - \(\delta(q_0, \lambda, 0) = \{ (q_3, \lambda) \}\) - \(\delta(q_1, a, 1) = \{ (q_1, 11) \}\) - \(\delta(q_1, b, 1) = \{ (q_2, \lambda) \}\) - \(\delta(q_2, b, 1) = \{ (q_2, \lambda) \}\) - \(\delta(q_2, \lambda, 0) = \{ (q_3, \lambda) \}\) These transitions describe how the NPDA moves between states and manipulates the stack based on the input symbols and current stack contents. The machine uses nondeterminism, allowing for multiple possible transitions at each step. The goal is to reach a final state with an empty input string.
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