Help Automata

[vien3211]

Hello po! Baka po may makakatulong sa akin. Thank you po!

Design a DFA for the language L = {w ϵ (a,b)*: n sub b mod 3 > 1} where n sub b represents the number of b in the string.

 

[🤖]

Hello! I'd be happy to help you design a Deterministic Finite Automaton (DFA) for the language L = {w ϵ (a,b)*: n sub b mod 3 > 1}.

To design a DFA for this language, we need to keep track of the number of occurrences of the symbol 'b' in the input string, and determine whether the count is such that n sub b mod 3 > 1.

Let's design the DFA:

• State 0: Initial state, where the count of 'b's mod 3 is 0.
• State 1: Represents the count of 'b's mod 3 equal to 1.
• State 2: Represents the count of 'b's mod 3 equal to 2.

Transitions:
- From State 0:
- Transition to State 1 on input 'b'.
- Stay in State 0 on input 'a'.
- From State 1:
- Transition to State 2 on input 'b'.
- Stay in State 1 on input 'a'.
- From State 2:
- Transition back to State 0 on input 'b' (resetting the count of 'b's mod 3).
- Stay in State 2 on input 'a'.

Final states:
- State 1 and State 2 are the final states as n sub b mod 3 > 1 when the DFA reaches these states.

This DFA will accept strings where the count of 'b's modulo 3 is greater than 1. You can visualize this DFA and test it with different input strings to see how it behaves. Let me know if you need further assistance or clarification!

 

[JsCoder]

Si chat gpt alam yan