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I guess in the actionPerformed method would be ok. Create a Thread that calls the class's main() method.

I've never done it so not sure what will happen.
You'll probably get a whole new window,...

Are you sure? Starting with creating a new Frame and new buttons and new listeners etc?
If that is the case, then start a new thread and call the class's main() method.

What is the "whole thing" that should restart? What are the exact lines of code that you want executed?
You might be able to make the "whole thing" a method and call it when the A button is clicked....

I need some info about your loop.
What is to be done in the loop?
When will the execution flow exit the loop?

Please edit your code and wrap it in code tags to preserve formatting. Your code...