They have finite resources so they can be modeled by finite number of state what is the same that a finite state machine. There are any proof that it is not true?Thanks.
Are real computers finite state machines?
computability;finite automata
Yes, real computers are finite state machines: they have finite memory so there's a finite number of states the machine can be in. One consequence of this is that a real computer can't recognise $\{a^nb^n\mid n\geq 0\}$.But hang on a second! you're saying, Any idiot could write a program that recognises that language.  Well, suppose your computer has $n$ bits of total storage (memory, disk, anything else you might have plugged in).  Even if you use all of that storage to count how many $a$'s you've seen, you can only count up to $2^n$.  That means your program can't tell the difference between a string that starts $a^{(2^n)}$ and one that starts $a^{(2^n+1)}$.But you need to consider the scale of these numbers. A typical computer has, say, 1TB of storage.  That means that $n=8\times 2^{40}$ and $2^n \approx 10^{2,600,000,000,000}$.  In contrast, the number of atoms in the universe is only about $10^{80}$ and some physicists estimate that the universe will cease to exist in any interesting way in only about $10^{100}$ years, which is about $3\times 10^{116}$ nanoseconds.  (Fun fact: the number of seconds in a year is within half a percent of $\pi\times 10^7$.)In other words, your 1GHz computer only has time to read in about $3\times 10^{116}$ characters before the heat death of the universe, and that's a looong way short of the number of characters you need to feed it to verify that it can't actually accept $a^nb^n$.  So, in practical terms, you can consider your computer to be a Turing machine instead of a finite state machine.