Draw an NFA (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 for the construction of a Non-deterministic Finite Automaton (NFA) without epsilon transitions. This NFA should accept all strings formed from the alphabet {a, b} that contain two or more occurrences of the symbol 'a'. Essentially, we need to design a machine that ensures the input string has at least two 'a's in any order and with any number of 'b's in between, before, or after them.
Answer
An NFA with 3 states: initial, one 'a' seen, and accept. Transitions on 'a' advance states; 'b' stays in the current state, and the accept state loops on all inputs.
The NFA will have three states. State 1 is the initial state. From State 1, on input 'a' go to State 2. State 1, on input 'b' remains in State 1. From State 2, on input 'a' go to State 3. State 2, on input 'b' remains in State 2. State 3 is the accept state. From State 3, on any input it remains in State 3.
Answer for screen readers
The NFA will have three states. State 1 is the initial state. From State 1, on input 'a' go to State 2. State 1, on input 'b' remains in State 1. From State 2, on input 'a' go to State 3. State 2, on input 'b' remains in State 2. State 3 is the accept state. From State 3, on any input it remains in State 3.
More Information
An NFA (Non-deterministic Finite Automaton) is a finite state machine where from each state and input symbol, there can be multiple possible next states.
Tips
A common mistake is forgetting that after seeing two 'a's, any subsequent input should still be accepted.
Sources
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