DES - Definition of 'State Automata'

State Automata:

A state automaton is a 1x5 tuple ($\mathcal{E}$, $\mathcal{X}$, $\Gamma$, $f$, $x_0$) where:

• $\mathcal{E}$ is a discrete set of events.
• $\mathcal{X}$ is a discrete set of states.
• $\Gamma$ is the domain.
  • For each $x\in \mathcal{X}$, $\Gamma \in \mathcal{E}$ is the set of events that are possible in the state $x$.
• $f$ : $\mathcal{X}\times \mathcal{E}\to \mathcal{X}$ is a transition function.
  • For each $x\in \mathcal{X}$, $e\in \Gamma$, $x^{\prime }=f(x,e)$ is the next state when the current state is $x$ and the next event is $e$.
• $x_0\in \mathcal{X}$ is the initial state

---

~Example: model of a queuing system