Final Answer
1. For the regular expression "bab*," the equivalent Finite Automaton would be a non-deterministic finite automaton (NFA) with three states. The states would represent different stages of processing the input, where the transition from state to state is determined by the characters of the input string.
2. For the regular expression "(a|b) (abc|a+b+c)," the equivalent Finite Automaton would be a deterministic finite automaton (DFA) with multiple states and transitions. The DFA would recognize valid strings that match the given regular expression pattern.
Explanation
For the regular expression "bab*," the corresponding Finite Automaton is designed to recognize strings that start with 'b,' followed by zero or more 'a's, and ending with 'b.' The automaton would have three states – one for the initial 'b,' one for the possible 'a's, and another for the final 'b.' Transitions between states would be determined by the input characters, creating a concise representation of the regular expression in automaton form.
The regular expression "(a|b) (abc|a+b+c)" involves an alternation operation (|) and concatenation. The equivalent Finite Automaton, in this case, would be a deterministic finite automaton (DFA) that processes the input string based on the defined patterns. The states in the automaton correspond to different stages of accepting or rejecting the input, and transitions are determined by the characters in the input string. The DFA provides a structured way of recognizing valid strings that adhere to the given regular expression.
In summary, converting regular expressions to equivalent Finite Automata involves designing automata that mimic the patterns specified by the regular expressions. The states and transitions in the automata correspond to different elements and operations in the regular expressions, providing a clear and systematic way to recognize strings that conform to the specified patterns.