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I'm looking on an example from my book of discrete mathematics and I've been reading a lot about these finite-state machines with output, however there is one thing I just still can't figure out. The example is here: Example

When looking at the first state (s0), I can see that by either using input 0 or 1, you can get from state s0 to either s1, or back to s0. The last column however, named "g" shows 1 and 0. at the first row and I can't seem to figure out what the meaning of this is.

I hope to get some help in here, and hopefully you can describe the idea of "g" using this exact example. Thanks in advance.

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Peterrr
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2 Answers2

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If I'm interpreting this right, from a given state an input results in both a change of state and an output. So from each state the light blue pair of numbers indicates the input and the respective output, and the arrow indicates the resulting state based on the input.

So, if you look at state $s0$, an input of $0$ moves you to state $s1$, and the pair along that arrow is $0,1$ meaning the output is $1$, so under $g$ in the table, an input of $0$ for state $s0$ results in a $1$.

Zimul8r
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In the model of "macine with output" you need a transition function and an output function.

Let $S$ the finite set of states, $\Sigma$ a finite set called the input alphabet and $\Lambda$ a finite set called the output alphabet.

We need

a transition function $F : S × Σ → S$ mapping pairs of a state and an input symbol to the corresponding next state

and

an output function $G : S × Σ → \Lambda$ mapping pairs of a state and an input symbol to the corresponding output symbol.

See Mealy machine.

Mauro ALLEGRANZA
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  • Ah yeah I see. Thanks for providing me the link to Mealy machines, it looks like thats alike it! – Peterrr Jun 03 '14 at 13:13