DES - Definition of 'State Automata with Output'

State Automata with Output:

A state automaton with outputs is a 7-tuple ($\mathcal{E}$, $\mathcal{X}$, $\Gamma$, $f$, $x_0$, $Y$, $g$), where:

• ($\mathcal{E}$, $\mathcal{X}$, $\Gamma$, $f$, $x_0$) is a state automaton
• $Y$ is a discrete set of outputs
• $g:\mathcal{X}\to Y$ is an output function
  • For each $x\in \mathcal{X}$, $y=g(x)$ is the system output when the current state is $x$

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Observation:

State automata are state automata with outputs where:

• $Y=\mathcal{X}$
• $g(x)=x$ for all $x\in \mathcal{X}$ (identity function)

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Observation:

State automata with outputs includes Moore Machines as a special case (when $\mathcal{X}$ is finite)

• Moore Machine are finite state machines used in sequential logic implementation

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~Example: model of a queuing system (cont’d)

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Observation:

In this example the model cannot be completed, its nonsense, so we can say that the model we designed is wrong for the system