How to Construct an NFA for a Language Defined by Ternary Notation Conditions?

[zeion]

Homework Statement

Hi,

I need to make an NFA for this language:

L = {s \in {0, 1, 2}* : the integer value pf s in ternary notation is one less than a multiple of 4}

Homework Equations

The Attempt at a Solution

I've written out and looked at the ternary notions for accepting strings, but can't seem to find a pattern. It seems that the last bit is in a cycling of 012 and the second last bit is a cycle of 120, 201, 012.

Is there a better approach to this?
Thanks

 

[KataKoniK]

Dear student,

Thank you for your post. Creating an NFA for this language can be challenging, but there are a few key things to keep in mind.

Firstly, remember that an NFA can have multiple states and transitions. It might help to draw out a state diagram to visualize the possible transitions for different inputs.

Secondly, think about what the language is asking for - an integer value in ternary notation that is one less than a multiple of 4. This means that the last two digits of the ternary number must be either 10 or 01, as these are the only two possibilities for a number that is one less than a multiple of 4.

With this in mind, you can start by creating two states - one for each possibility of the last two digits. From these states, you can create transitions for the rest of the string, keeping in mind that the last two digits must remain either 10 or 01.

I hope this helps guide you in the right direction. Don't be afraid to experiment and try different approaches. Best of luck!