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But that argument is not interesting. "We can't count arbitrarily high because the universe is finite." Yeah, duh. (Observable universe, for the pedants.) It's
by tylerhou 3y ago
But that argument is not interesting. "We can't count arbitrarily high because the universe is finite." Yeah, duh. (Observable universe, for the pedants.)
It's more interesting to ask: suppose you did have a magical stick of RAM that had infinite storage, and suppose you augmented your computer to store and query that memory. Then -- yes -- your computer could determine whether any number, however large, is prime. An FSM could not.
- dheera 3y agoIf you have an infinite stick of RAM, regular expressions wouldn't be FSMs, either, they could have infinite state space. They would terminate in finite time that is exponential in the size of the prime but nevertheless would still halt.
- School-Cotton 3y agoThe point being made is that “regular expressions”, in the original CS meaning, do not have stack space or anything analogous. “Regular expressions” in modern programming practice are often different and more powerful, of course.
- kaba0 3y agoA finite state machine can’t have infinite state space.. also, you can write a finite Turing program that does exactly that, but you can’t write a finite description of an “infinite” state space, which is the whole point. Ad absurdum everything would be computable (recognizable) by FSMs, simply by listing all the infinite number of possibilities. listOfAllPrimes.concat(“|”), here you are..
- funcDropShadow 3y agoNo, you could create arbitrarily large FSMs, but there are no infinite finite state machines.