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

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).For the language X^aY^b, Give the transition function