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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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    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).2012-06-09

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