3. (.) Build the intersection machine for the two following languages described by the two following FAs FA2 FA1 a a b. а, b (x4 + a ,b a (x1 b y2 a b x3 4. (.) Prove that the language L={a"b?"} is non-regular.
3. (.) Build the intersection machine for the two following languages described by the two following FAs FA2 FA1 a a b. а, b (x4 + a ,b a (x1 b y2 a b x3 4. (.) Prove that the language L={a"b?"} is non-regular.
Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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### Problem 3
**Task:** Build the intersection machine for the two following languages described by the two following FAs (Finite Automata).
**FA1 Description:**
- States: x1, x2, x3, x4
- Transitions:
- x1 to x2 via 'a'
- x1 to x3 via 'b'
- x2 to x2 via 'b'
- x2 to x4 via 'a'
- x3 to x3 via 'b'
- x4 to x4 via 'a', 'b'
- x3 to x4 via 'a'
**FA2 Description:**
- States: y1, y2
- Transitions:
- y1 to y1 via 'b'
- y1 to y2 via 'a'
- y2 to y2 via 'a', 'b'
**Text:** Build the intersection machine for the two following languages described by the two following FAs.
### Problem 4
**Task:** Prove that the language \( L = \{ a^n b^{2n} \} \) is non-regular.
---
**Explanation of Diagrams:**
1. **FA1 Diagram:**
- It contains four states arranged in a diamond shape.
- Arrows indicate transitions between states based on input symbols 'a' and 'b'.
- Transition from x1 directly to x4 via either 'a' or 'b' is highlighted.
2. **FA2 Diagram:**
- It consists of two states.
- State y1 loops on 'b' and transitions to y2 on 'a'.
- State y2 loops on both 'a' and 'b'.
This explanation is intended to aid in understanding the construction of an intersection machine for the automata and to support learning about regular and non-regular languages.
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