In reference to the Chomsky hierarchy (and automatas), Which is the linear feedback shift register Languages/automaton? The Chomsky hierarchy is a guideline on language expressive power. The linear feedback shift register is a very interesting "element" to structure a language and there is a large theoretical literature. 

In reference to the Chomsky hierarchy (and automata), which is the linear feedback shift register languages/automaton ?
It has a finite memory, so it's just a DFA (or some of the output-producing variants). If you allow a growing/shrinking feedback register, it is probably equivalent to a Turing machine.