How can a Moore machine be converted into an equivalent Mealy machine and vice versa?

Question

Moore machine is a finite-state machine whose output values are determined by its current state only.

Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs

I just don't see what can be changed for one to be proved equivalent to other.

Answer 1

I'm not sure this'll help, as I'm not very familiar with comp sci, but consider a general discrete example $$x_{k+1} = f(x_k), \quad k=0,1,...,n-1 \qquad (1.1)$$

where $f(x_k)$ determines the next state.

Then consider a different discrete case where we have a input variable $a_k$ so that the above becomes

$$x_{k+1} = f(x_k,a_k), \quad k = 0,1,...,n-1 \qquad (1.2)$$

From a quick Wikipedia read, you may change Eq (1.1) so that we have $f_k$ instead of $f$... so we have multiple functions and we may make them produce equivalent results to the Eq. (1.2) $$x_{k+1} = f_k(x_k), \quad k = 0,1,...,n-1 \quad (1.3)$$

Here is a source I read.