It seems to me that any problem whose solution requires finite memory can be emulated on a Finite State Machine . This would make those problems that can't be solved by a Finite State Machine to require infinite memory ( like general multiplication of integers ).
My question is what "infinite memory" really means if "infinite" is used in some "completed sense" ( its the negation of finite ). To me the notion of "infinite memory" seems to me so weird and well-defined. How can a problem that requires infinite memory be computable ?
Can anyone help me clarify that ?
Thanks a lot in advance .