Math Help - Define the constraints on α and β in a finite state rewrite rule of the form α --> β?

1. Define the constraints on α and β in a finite state rewrite rule of the form α --> β?

This question came up in a test I had recently and I didn't know how to answer it. Any advice is greatly appreciated.

Oh. The other question I also had dificulties with was...

For the language X^aY^b, Give the transition function??? (Where ^ means 'to the power of).

Thanks again

2. Define the constraints on α and β in a finite state rewrite rule of the form α --> β?
I am not sure, but maybe it's about regular grammars? The reason I am thinking this is that "finite state" probably pertains to finite state automata (FSA) and "rewrite" has to do with grammars. Regular grammars have the same expressive power as FSA.

For the language X^aY^b, Give the transition function
You probably need to come up with an FSA that accepts this language and write its state-transition function (see the "Mathematical model" section on finite-state machines).