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**Problem Statement:**

Design a Finite State Machine (FSM) over the alphabet {0, 1} that accepts strings which do **not** have "111" as a substring. For example, the strings "1011" and "000110" will be accepted, but "011100" and "111101" will not.

**Explanation:**

- The aim is to construct an FSM that processes binary strings and accepts only those that do not contain the sequence "111".
- The FSM should transition through states based on input symbols (0 or 1) and reach an accept state if the forbidden pattern does not occur.
- By definition, the FSM must halt in a non-accept state if "111" is encountered at any point while reading the input.

**Examples:**

- **Accepted Strings:** "1011", "000110"
- **Rejected Strings:** "011100", "111101"

Design your FSM with these rules in mind, and consider using a state diagram to represent transitions between states.
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Transcribed Image Text:**Problem Statement:** Design a Finite State Machine (FSM) over the alphabet {0, 1} that accepts strings which do **not** have "111" as a substring. For example, the strings "1011" and "000110" will be accepted, but "011100" and "111101" will not. **Explanation:** - The aim is to construct an FSM that processes binary strings and accepts only those that do not contain the sequence "111". - The FSM should transition through states based on input symbols (0 or 1) and reach an accept state if the forbidden pattern does not occur. - By definition, the FSM must halt in a non-accept state if "111" is encountered at any point while reading the input. **Examples:** - **Accepted Strings:** "1011", "000110" - **Rejected Strings:** "011100", "111101" Design your FSM with these rules in mind, and consider using a state diagram to represent transitions between states.
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