SUBJECT - THEORY OF COMPUTING THANKS IN ADVANCE **Transcription for Educational Website:**---### 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.

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)

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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Question

SUBJECT - THEORY OF COMPUTING

THANKS IN ADVANCE

**Transcription for Educational Website:**

---

### 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.

Theory that deals with fundamental questions around what problems can and cannot be solved using computation and uses a model of computation to understand the degree to which computers can assist in solving problems. There are three main branches of this subject: automata theory and formal languages, computational complexity theory, and computability theory.

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