Construct a DFA accepting binary strings such that the third symbol from the right end is 1.
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To construct a DFA that accepts binary strings where the third symbol from the right is 1:

1. **States**: \( q_0 \) (start), \( q_1 \), \( q_2 \), \( q_3 \) (accept), \( q_4 \) (trap).
2. **Transitions**:
   - From \( q_0 \):
     - On `0` or `1`, go to \( q_1 \).
   - From \( q_1 \):
     - On `0` or `1`, go to \( q_2 \).
   - From \( q_2 \):
     - On `1`, go to \( q_3 \) (accept).
     - On `0`, go to \( q_4 \) (trap).
   - From \( q_3 \):
     - Stay in \( q_3 \) on any input.
   - From \( q_4 \):
     - Stay in \( q_4 \) on any input.
3. **Accepting state**: \( q_3 \).

This DFA checks if the third symbol from the right is `1` and accepts the string if it is.

Would you like more details or have any questions?

Here are 5 related questions:
1. Do you need a visual diagram of this DFA?
2. Would you like an explanation of DFA state transitions?
3. Need help with another DFA construction problem?
4. Curious about converting this DFA to a regex?
5. Want to explore non-binary alphabet DFAs?

**Tip:** Understanding how DFAs process input one symbol at a time can help in constructing them efficiently.

Learn how to construct a Deterministic Finite Automaton (DFA) that accepts binary strings where the third symbol from the right end is 1. This DFA involves states, transitions, and acceptance criteria, crucial for understanding Finite Automata theory.

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