Can a finite state machine have infinitely many states?

No. The definition of Turing machines requires that the finite-state control unit have a finite number of states. It’s not allowed to have an infinite number of states. A machine that could have infinitely many states in its control could accept any language (unlike a Turing machine).

Why is the halting problem unsolvable?

A key step in showing that incompleteness is natural and pervasive was taken by Alan M. Turing in 1936, when he demonstrated that there can be no general procedure to decide if a self-contained computer program will eventually halt.

Is there Infinite state machine?

A computational machine whose complete description is inextricably linked to a description of the universe. No, InfiniteStateMachine is a StateMachine that doesn’t have a finite number of states (whether we know how many or not). …

Can a Turing machine solve halting problem?

In 1936, Alan Turing proved that the halting problem over Turing machines is undecidable using a Turing machine; that is, no Turing machine can decide correctly (terminate and produce the correct answer) for all possible program/input pairs. …

Can a finite state machine run infinitely?

Turing machines use finite means In it he categorizes machines into those that are finite (such as finite state machines) and those that are infinite (such as Turing machines). So they are infinite in the same sense that Turing machines are infinite).

Why are finite state machines considered to be abstract?

It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a transition. This is because an FSM’s memory is limited by the number of states it has.

Which types of problems can be solved by using finite state machines?

Finite state automata generate regular languages. Finite state machines can be used to model problems in many fields including mathematics, artificial intelligence, games, and linguistics. A system where particular inputs cause particular changes in state can be represented using finite state machines.

What is halting problem in Turing machine TM )?

The Halting Problem is the problem of deciding or concluding based on a given arbitrary computer program and its input, whether that program will stop executing or run-in an infinite loop for the given input.

Is it possible to create an infinite state machine?

Yes, you could. An infinite state machine could hold an infinite amount of information, so you could have a machine that “hardcodes” the answer to every possible Halting Problem input. Of course, you wouldn’t be able to compute what this infinite state machine looks like from any lesser finite state machine.

Is the halting problem on finite state automata decidable?

The halting problem on Turing machines is undecidable. Conversely, the halting problem on finite state automata is easily decidable; all finite state automata halt. Thus it’s important to specify the model. The halting problem on usual computers is also decidable.

Can the class of infinite state machines recognize every language?

No, the class of infinite-state machines can recognize any language at all or, equivalently, any power set of the natural numbers. The class of ordinary Turing machines cannot. Any Turing machine has a finite description and, as such, a class of Turing machines can recognize only countably many languages.

Is there a Turing machine with an infinite number of States?

You can’t define a Turing machine with an infinite number of states any more than you can define a finite state machine with an infinite number of states — infinity is neither a thing, a quantity, nor a process; infinity is a quality.