Final answer:
The student asked for a DFA that accepts strings where the third symbol from the right is a 0. The DFA should track the last three symbols of the string and must have an accepting state that represents sequences ending with any combination followed by '0' and any two symbols.
Step-by-step explanation:
The student is requesting a deterministic finite automaton (DFA) that accepts the language of all strings where the third symbol from the right is a 0. When constructing this DFA, it's important to account for the last three symbols in the strings, as their configuration determines the string's acceptance. Below is a general description of the required DFA:
- Begin in an initial state where we don't yet know the third symbol from the right.
- Transit to different states based on the input, tracking the last two symbols.
- Reach an accepting state if, following the transition based on the next (third from last) input, a 0 is read.
- Ensure all strings that do not have a third symbol from the right as 0 lead to a non-accepting state.
To create this DFA, one could construct states that represent the knowledge of what the last three symbols are as we read the string from left to right. The states would transition in such a fashion that once the DFA processes the antepenultimate symbol, if it's a 0, the DFA would be directed to an accepting state, provided that the last two symbols (any combination of 0s or 1s) are processed without leaving the accepting states. This design ensures that any string ending with any combination followed by '0' and then two more symbols (0 or 1) will be accepted.