Draw a DFA (without ε-moves) that accepts all strings over the alphabet {a, b} that contain at least two a’s.
Understand the Problem
The question asks to design a Deterministic Finite Automaton (DFA) that recognizes strings over the alphabet {a, b} containing at least two 'a's. This involves creating a state diagram with transitions for 'a' and 'b', ensuring the DFA reaches an accepting state only after encountering at least two 'a's in the input string.
Answer
A DFA that accepts strings with at least two 'a's over {a, b} needs states tracking the count of 'a's and transitions for 'a' and 'b', with the accept state reached after two 'a's.
The Deterministic Finite Automaton (DFA) should have states representing the number of 'a's encountered (0, 1, 2 or more). Transitions are based on the input alphabet {a, b}. The accepting state is the one reached after at least two 'a's are read.
Answer for screen readers
The Deterministic Finite Automaton (DFA) should have states representing the number of 'a's encountered (0, 1, 2 or more). Transitions are based on the input alphabet {a, b}. The accepting state is the one reached after at least two 'a's are read.
More Information
A DFA is used to recognize patterns, such as 'at least two a's', in strings. Each state represents the automaton's memory of what it has read, and the transitions dictate how to update that memory as it reads the string.
Tips
A common mistake is not accounting for all possible transitions from each state for each character in the alphabet {a, b}. Another mistake is not having a 'dead state' or sink state if the conditions can never be fulfilled.
Sources
- DFA that Accepts All the Strings With At Least 1 'a' and Exactly 2 b's - geeksforgeeks.org
- Solved For ∑ = {a, b}, construct dfa's that accept the sets | Chegg.com - chegg.com
- A finite automaton that accepts at least three - a - s and at least two - b - math.stackexchange.com
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