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PDA for the given language.

PDA for the given language.

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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build a PDA for the given language.

The image provides details on two Pushdown Automata (PDA) related to the language \( \{a^{3n}b^n : n \geq 0\} \). Below is a description for each section and diagram: 1. **Language Definition:** - The set is defined as \( \{a^{3n}b^n : n \geq 0\} \). 2. **First PDA:** - There is a checkbox labeled: "The following PDA accepts L." - **Diagram Explanation:** - Two states are shown in circles, labeled \( q0 \) and \( q1 \). - An arrow with a triangle points to state \( q0 \), indicating the initial state. - A loop on \( q0 \) reads \( a, \varepsilon : a \), meaning it processes an 'a' by pushing 'a' onto the stack. - A transition from \( q0 \) to \( q1 \) is labeled \( b, aaa : \varepsilon \), meaning it processes a 'b' by popping three 'a's from the stack. - A loop on \( q1 \) with \( b, aaa : \varepsilon \) performs the same action at state \( q1 \). 3. **Second PDA:** - There is a checkbox labeled: "The following PDA accepts L." - **Diagram Explanation:** - Similar structure with states \( q0 \) and \( q1 \). - Initial state depicted by an arrow with a triangle pointing to \( q0 \). - A loop on \( q0 \) reads \( a, \varepsilon : a \). - A transition from \( q0 \) to \( q1 \) reads \( \varepsilon, \varepsilon : \varepsilon \), indicating a spontaneous transition without input or stack operation. - A loop on \( q1 \) reads \( b, aaa : \varepsilon \). 4. **Determinism Checkbox:** - A checkbox labeled: "The provided PDAs above are both deterministic." Each PDA has similar structures but different transitions for processing the input to determine acceptance of the given language.
Transcribed Image Text:The image provides details on two Pushdown Automata (PDA) related to the language \( \{a^{3n}b^n : n \geq 0\} \). Below is a description for each section and diagram: 1. **Language Definition:** - The set is defined as \( \{a^{3n}b^n : n \geq 0\} \). 2. **First PDA:** - There is a checkbox labeled: "The following PDA accepts L." - **Diagram Explanation:** - Two states are shown in circles, labeled \( q0 \) and \( q1 \). - An arrow with a triangle points to state \( q0 \), indicating the initial state. - A loop on \( q0 \) reads \( a, \varepsilon : a \), meaning it processes an 'a' by pushing 'a' onto the stack. - A transition from \( q0 \) to \( q1 \) is labeled \( b, aaa : \varepsilon \), meaning it processes a 'b' by popping three 'a's from the stack. - A loop on \( q1 \) with \( b, aaa : \varepsilon \) performs the same action at state \( q1 \). 3. **Second PDA:** - There is a checkbox labeled: "The following PDA accepts L." - **Diagram Explanation:** - Similar structure with states \( q0 \) and \( q1 \). - Initial state depicted by an arrow with a triangle pointing to \( q0 \). - A loop on \( q0 \) reads \( a, \varepsilon : a \). - A transition from \( q0 \) to \( q1 \) reads \( \varepsilon, \varepsilon : \varepsilon \), indicating a spontaneous transition without input or stack operation. - A loop on \( q1 \) reads \( b, aaa : \varepsilon \). 4. **Determinism Checkbox:** - A checkbox labeled: "The provided PDAs above are both deterministic." Each PDA has similar structures but different transitions for processing the input to determine acceptance of the given language.
Expert Solution
Step 1: Given 

Consider the given language. 
L={a3nbn* : n>=0 } 

i.e number of a's in w is equal to trice the number of b's in w and all a's will be at the 
beginning of the input and all the b's will be at the end of the input.

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