4₁: Name the accept states in the machine L₂' U L₁ (read as: L₂ prime union L₁) b q1 L₂: q0 q2 b 90 a b q2 D q1 6 C

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**Finite State Machines L1 and L2**

In this exercise, we are asked to identify the accept states in the machine \( L_2' \cup L_1 \) (read as: \( L_2 \) prime union \( L_1 \)).

Two finite state machines (FSMs) are given, labeled \( L_1 \) and \( L_2 \). 

### FSM \( L_1 \):
- **States**: \( q0 \), \( q1 \), and \( q2 \)
- **Transitions**:
    - From \( q0 \) to \( q1 \) on 'a'
    - From \( q1 \) to \( q2 \) on 'a'
    - From \( q2 \) to \( q0 \) on 'a'
    - From \( q0 \) to \( q0 \) on 'b'
    - From \( q0 \) to \( q2 \) on 'b'
    - From \( q2 \) to \( q2 \) on 'b'
    - From \( q2 \) to \( q1 \) on 'b'
- The start state is \( q0 \).
- There are no accept states explicitly marked in \( L_1 \).

### FSM \( L_2 \):
- **States**: \( q0 \), \( q1 \), and \( q2 \)
- **Transitions**:
    - From \( q0 \) to \( q1 \) on 'a'
    - From \( q1 \) to \( q2 \) on 'a'
    - From \( q2 \) to \( q0 \) on 'a'
    - From \( q2 \) to \( q2 \) on 'b'
    - From \( q1 \) to \( q1 \) on 'b'
    - From \( q1 \) to \( q0 \) on 'b'
    - From \( q0 \) to \( q2 \) on 'b'
- The start state is \( q0 \).
- Accept states are \( q0 \), \( q1 \), and \( q2 \).

### Diagram Description
The diagrams for \( L_1 \) and \( L_2 \) are labeled with states represented as circles and transitions as arrows. The initial states are marked with an incoming arrow (without
Transcribed Image Text:**Finite State Machines L1 and L2** In this exercise, we are asked to identify the accept states in the machine \( L_2' \cup L_1 \) (read as: \( L_2 \) prime union \( L_1 \)). Two finite state machines (FSMs) are given, labeled \( L_1 \) and \( L_2 \). ### FSM \( L_1 \): - **States**: \( q0 \), \( q1 \), and \( q2 \) - **Transitions**: - From \( q0 \) to \( q1 \) on 'a' - From \( q1 \) to \( q2 \) on 'a' - From \( q2 \) to \( q0 \) on 'a' - From \( q0 \) to \( q0 \) on 'b' - From \( q0 \) to \( q2 \) on 'b' - From \( q2 \) to \( q2 \) on 'b' - From \( q2 \) to \( q1 \) on 'b' - The start state is \( q0 \). - There are no accept states explicitly marked in \( L_1 \). ### FSM \( L_2 \): - **States**: \( q0 \), \( q1 \), and \( q2 \) - **Transitions**: - From \( q0 \) to \( q1 \) on 'a' - From \( q1 \) to \( q2 \) on 'a' - From \( q2 \) to \( q0 \) on 'a' - From \( q2 \) to \( q2 \) on 'b' - From \( q1 \) to \( q1 \) on 'b' - From \( q1 \) to \( q0 \) on 'b' - From \( q0 \) to \( q2 \) on 'b' - The start state is \( q0 \). - Accept states are \( q0 \), \( q1 \), and \( q2 \). ### Diagram Description The diagrams for \( L_1 \) and \( L_2 \) are labeled with states represented as circles and transitions as arrows. The initial states are marked with an incoming arrow (without
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