M = ({90, 91, 92, 93, y}, {0, 1}, {0, 1, $, #, }, 8, qo, {y}), where 8 =

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**Question:**

(2) Define M with a transition diagram. You may use JFLAP to create this diagram. Compare your diagram with the following and verify its correctness. Note that there can be multiple correct answers.

M = ({q₀, q₁, q₂, q₃, y}, {0, 1}, {0, 1, $, #, □}, δ, q₀, {y}), where δ =

**Transition Diagram Description:**

- **States:** q₀, q₁, q₂, q₃, and y
- **Initial State:** q₀ (indicated by an arrow pointing to q₀)
- **Final State:** y (indicated by a double circle)
- **Alphabet:** {0, 1}
- **Tape Symbols:** {0, 1, $, #, □}

**Transitions:**

1. **q₀:**
   - `0; 0, R`: Transition to q₀ when reading '0', writes '0', moves right.
   - `$; $, R`: Transition to q₁ when reading '$', writes '$', moves right.

2. **q₁:**
   - `#; #, R`: Stay in q₁ when reading '#', writes '#', moves right.
   - `0; 0, R`: Stay in q₁ when reading '0', writes '0', moves right.
   - `1; #, L`: Transition to q₂ when reading '1', writes '#', moves left.

3. **q₂:**
   - `#; #, L`: Stay in q₂ when reading '#', writes '#', moves left.
   - `0; 0, L`: Stay in q₂ when reading '0', writes '0', moves left.
   - `$; $, R`: Transition to q₀ when reading '$', writes '$', moves right.

4. **q₀ (loop):**
   - `#; #, R`: Stay in q₀ when reading '#', writes '#', moves right.

5. **q₃:**
   - `#; #, R`: Stay in q₃ when reading '#', writes '#', moves right.
   - `□; □, R`: Transition to y when reading '□', writes '□', moves right.

**Options to Verify:
Transcribed Image Text:**Question:** (2) Define M with a transition diagram. You may use JFLAP to create this diagram. Compare your diagram with the following and verify its correctness. Note that there can be multiple correct answers. M = ({q₀, q₁, q₂, q₃, y}, {0, 1}, {0, 1, $, #, □}, δ, q₀, {y}), where δ = **Transition Diagram Description:** - **States:** q₀, q₁, q₂, q₃, and y - **Initial State:** q₀ (indicated by an arrow pointing to q₀) - **Final State:** y (indicated by a double circle) - **Alphabet:** {0, 1} - **Tape Symbols:** {0, 1, $, #, □} **Transitions:** 1. **q₀:** - `0; 0, R`: Transition to q₀ when reading '0', writes '0', moves right. - `$; $, R`: Transition to q₁ when reading '$', writes '$', moves right. 2. **q₁:** - `#; #, R`: Stay in q₁ when reading '#', writes '#', moves right. - `0; 0, R`: Stay in q₁ when reading '0', writes '0', moves right. - `1; #, L`: Transition to q₂ when reading '1', writes '#', moves left. 3. **q₂:** - `#; #, L`: Stay in q₂ when reading '#', writes '#', moves left. - `0; 0, L`: Stay in q₂ when reading '0', writes '0', moves left. - `$; $, R`: Transition to q₀ when reading '$', writes '$', moves right. 4. **q₀ (loop):** - `#; #, R`: Stay in q₀ when reading '#', writes '#', moves right. 5. **q₃:** - `#; #, R`: Stay in q₃ when reading '#', writes '#', moves right. - `□; □, R`: Transition to y when reading '□', writes '□', moves right. **Options to Verify:
**Design a Turing machine \( M \) that decides the language \( L = \{0^n1^n \mid n \geq 1\}.****

In this task, we are asked to create a Turing machine that can recognize the language consisting of strings where the number of 0s is equal to the number of 1s, and there is at least one occurrence of each. The strings must be formatted such that all 0s appear before any 1s.
Transcribed Image Text:**Design a Turing machine \( M \) that decides the language \( L = \{0^n1^n \mid n \geq 1\}.**** In this task, we are asked to create a Turing machine that can recognize the language consisting of strings where the number of 0s is equal to the number of 1s, and there is at least one occurrence of each. The strings must be formatted such that all 0s appear before any 1s.
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