Construct a DFA that accepts all strings over the alphabet Σ = {a, b} that contain only a’s. Define the DFA using its 5-tuple. Draw the state diagram of the DFA.
Understand the Problem
The question is asking us to construct a Deterministic Finite Automaton (DFA) for the given alphabet that only accepts strings composed entirely of 'a's. We need to specify the DFA using its 5-tuple representation, which includes the states, alphabet, transition function, start state, and accept states. Additionally, we're asked to draw the state diagram of the DFA.
Answer
Define DFA with Q = {q0, q1}, Σ = {a, b}, q0 = q0, F = {q0}, δ(q0, a) = q0, δ(q0, b) = q1 (trap).
To construct a DFA for strings that only contain 'a's over the alphabet Σ = {a, b}, define M = (Q, Σ, δ, q0, F), where Q = {q0, q1}, Σ = {a, b}, q0 = q0, F = {q0}, and δ consists of δ(q0, a) = q0 and δ(q0, b) = q1 with q1 being a non-accepting trap state.
Answer for screen readers
To construct a DFA for strings that only contain 'a's over the alphabet Σ = {a, b}, define M = (Q, Σ, δ, q0, F), where Q = {q0, q1}, Σ = {a, b}, q0 = q0, F = {q0}, and δ consists of δ(q0, a) = q0 and δ(q0, b) = q1 with q1 being a non-accepting trap state.
More Information
This DFA accepts strings composed solely of 'a's and transitions to a trap state on encountering 'b', ensuring any strings containing 'b' are rejected.
Tips
A common mistake is not creating a trap state. It's important to ensure that once a 'b' is encountered, the state transitions to a non-accepting state.
Sources
- Deterministic Finite State Automata - Dr. Swaminathan J - swaminathanj.github.io
- Solved Question 1 (a) A deterministic finite automaton (DFA) - Chegg - chegg.com
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