I am struggling on this one question, where it is asking to define an XOR automata which is defined as an NFA and it is defined as the following:
N accepts the string x if the number of distinct accepting states that can be reached by a path labeled with x is odd.
I'm supposed to prove that any languages accepted by the XOR automata is regular and that any regular language can be accepted by the XOR automata.
Can anyone explain to me how I may be able to go about starting this proof? Thanks.