Final answer:
The regular expression for the language described is 1(0+1)*0, representing strings that start with 1 and end with 0 with at least three digits. A three-state DFA can be constructed for this, indicating that the language is regular as it conforms to a finite automaton.
Step-by-step explanation:
The language described requires strings that start with 1 and end with 0 and have at least three digits. This implies that the middle section of the string can be either 0s or 1s and can be of any length, including possibly empty.
1. Regular expression for the language
The regular expression that represents this language is 1(0+1)*0. This expression indicates that the string starts with a 1, followed by zero or more occurrences of either 0 or 1, and ends with a 0.
2. DFA diagram for this language
A DFA (Deterministic Finite Automaton) for this language can be constructed as follows:
- State 1: Start state, accepts '1' and moves to state 2.
- State 2: Intermediate state, accepts '0' or '1' and remains here.
- State 3: Accepting state after receiving another '1' or '0' from state 2, but stays in state 2 for '1', and only transitions to state 3 upon receiving a '0'.
Note: The actual drawing of the DFA is not possible to represent in pure text or json format, but a simple 3-state diagram with transitions as described above can be constructed.
3. Is the language regular?
Yes, the language is regular. A language is considered regular if it can be expressed by a regular expression or constructed using a finite automaton, which is the case here with the provided regular expression and the possibility to build a DFA.