Is the Markov chain the same as a finite state machine?

Question

Is the final machine just an implementation of the Markov chain? What are the differences between the two?

Answer 1

Markov chains can be represented by finite state machines. The idea is that the Markov chain describes a process in which the transition to a state at time t + 1 depends only on the state at time t. The main thing to keep in mind is that transitions in the Markov chain are more probabilistic than deterministic, which means that you cannot always say with full confidence what will happen at time t + 1.

Wikipedia articles on machines with a finite number of states have a subsection on processes with a finite Markov chain ; I would recommend reading it for more information. In addition, the Wikipedia article on Markov chains contains a brief sentence describing the use of finite state machines in representing Markov chains. It states:

A state machine can be used as a representation of a Markov chain. Assuming a sequence of independent and identically distributed input signals (for example, characters from the binary alphabet selected by tossing coins), if the machine is in state y at time n, then the probability that it will move to state x at time n + 1 depends only from the current state.

Answer 2

While the Markov chain is a machine with a final state, it differs in that its transitions are stochastic, i.e. random and described by probabilities.

Answer 3

Both are similar, but the other explanations here are slightly flawed. Only finite Markov chains can be represented by FSM. Markov chains admit an infinite space of states. As noted, the transitions of the Markov chain are described by probabilities, but it is also important to note that the transition probabilities can depend only on the current state. Without this restriction, it will be called the "discrete stochastic process of time."

Answer 4

Read these docs:

Links between probabilistic automata and hidden Markov models (Pierre Dupont) http://www.info.ucl.ac.be/~pdupont/pdupont/pdf/HMM_PA_pres_n4.pdf

[Handbook of brain theory and neural networks] Hidden Markov models and other finite state machines for sequence processing http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.85.3344&rep=rep1&type=pdf

Answer 5

I believe this should answer your question:

https://en.wikipedia.org/wiki/Probabilistic_automaton

And you go to the right idea - they are almost the same: subsets, supersets and modifications depending on which adjective describes a circuit or an automaton. Automata, as a rule, also accept data, but I’m sure that there were papers using “Markov chains” with inputs.

Think, Gaussian distribution versus normal distribution are the same ideas in different areas. Automata relate to computer science, Markov relates to probability and statistics.

Answer 6

If we leave the internal working parts aside, the final state machine looks like a simple value, and the chain of marks looks like a random value (add probability over the simple value). Thus, the answer to the original question is no, they do not match. In a probabilistic sense, the Markov chain is a continuation of the machine of the final state.

Answer 7

I think most answers are not suitable. A Markov process is generated by a (probabilistic) state machine, but not every process generated by a probabilistic state machine is a Markov process. For example, hidden Markov processes basically coincide with the processes generated by probabilistic machines of final states, but not every hidden Markov process is a Markov process.