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I have the following simple automata:

enter image description here

What I'm looking for is a formal description of this based on the definition here

$A=(\Sigma,\Gamma,S,s_0,\delta,\omega, F)$

How to declare all the variables? Or do I need a different definition for this kind of automata?

What I got is the following, but I'm not sure about most parts of it:

$\Sigma = \{i_{in}\}$
$\Gamma = \{i_{out}\}$ $S = \{Init, Inc, Reset\}$ with $s_0 = Init$.
$\delta$ somehow contains $\Delta = \{(Init, Inc), (Inc, Init), (Init, Reset), (Reset, Init)\} $ and has to be depend on $\Sigma$.

And how is $\omega$ defined?

Please tell me how to do this right, or maybe show me some tutorials that might help. Thanks

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Sorry, I forgot to mention that i > 0 is a guard, and the transition can only be fired when i is bigger than 0 and the blue labels are updated, where i = 0 sets i to 0 and i++ increases the value of i by 1 –  Tarion Jun 7 '12 at 14:29
    
The picture is not entirely clear to me. Can you describe in words what the machine is supposed to do? If you mean for it to be a finite state automaton, according to the usual definition, I would interpret your picture as follows: the machine reads a number, $a_0$. If $a_0\leq 0$, it outputs $a_1 + 1$, then begins again with $a_2$. If $a_0>0$, it outputs $0$, then begins again with $a_2$. It accepts an input if the input consists of an even number of digits. –  Alex Kruckman Jun 9 '12 at 17:40
    
It seems unlikely that this was what was intended, in which case you won't be able to express your machine using the formalism you've described (input alphabet, output alphabet, state set, initial state, transition function, output function, acceptance condition). –  Alex Kruckman Jun 9 '12 at 17:42
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1 Answer

up vote 0 down vote accepted

I found the solution in a description of the tool I'm using: Uppaal New Tutorial

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