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

Question

Is a finite state machine just an implementation of a Markov chain? What are the differences between the two?

Answer 1

Markov chains can be represented by finite state machines. The idea is that a 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 the transitions in a Markov chain are probabilistic rather than deterministic, which means that you can't always say with perfect certainty what will happen at time t+1.

The Wikipedia articles on Finite-state machines has a subsection on Finite Markov-chain processes, I'd recommend reading that for more information. Also, the Wikipedia article on Markov chains has a brief sentence describing the use of finite state machines in representing a Markov chain. That states:

A finite state machine can be used as a representation of a Markov chain. Assuming a sequence of independent and identically distributed input signals (for example, symbols from a binary alphabet chosen by coin tosses), if the machine is in state y at time n, then the probability that it moves to state x at time n + 1 depends only on the current state.

Answer 2

Whilst a Markov chain is a finite state machine, it is distinguished by its transitions being stochastic, i.e. random, and described by probabilities.