# Is it possible to convert LBA into DFA?

Today I learned about an abstract class of machines called linear bounded automata.

It is intended to model real-world computers that have a limited amount of memory. I have always thought that real computers are DFAs due to the finite memory (but the DFA is a terribly poor abstraction).

Is it possible to convert LBA into an equivalent DFA by making every possible tape configuration into a state of the DFA?

In particular, LBAs can accept non-regular languages, such as $$\{a^nb^n\mid n\geq 0\}$$ so there are LBAs that can't be converted to a single DFA.
Yes, you just modelled the LBA by a finite state device. You have to decide what are the actions of that model, probably the instructions of the LBA ("in state $$q$$ on reading $$a$$ on the tape do ...").