Transducer for water pouring problem?

Is it possible to create a finite-state transducer for the Water Pouring Problem?
The input set of alphabets can be a set of set of two values like {m,n} where m and n can be the amount of water in jugs, and the output set of alphabets can be {0,1}. The output will be 0 if the string ends in a non-final state and 1 if the string end in a final state.
I suppose this should be possible to create as every output can be created using finite sequence of steps and the machine created should be able to list out all possible solutions to any amount of water in any jug just by changing the final state of the machine.
Are all my assumptions and suppositions correct?