## 5 Events Depending on Multivalued Signals  
This section presents the set of events associated with multivalued signals, where a range of integer values can be read (digital inputs). Similarly to the analysis of Boolean signals, Table 2 presents the definition of four sets of five events generated through the evolution analysis of multivalued signals, providing updated definitions for the former set composed of \(Up\), \(Down\), \(UpOrDown\), \(UpDown\), and \(DownUp\) events (which were initially proposed in [1,12,25]), where a threshold value \(k\) is used for comparison with a predefined level. A second set of events is proposed associated with similar events constrained by the verification of conditions to fire the transition with whom they are associated; this set is composed of \(UpTrigger\), \(DownTrigger\), \(UpOrDownTrigger\), and \(DownUpTrigger\), also considering a value \(k\) for comparison. Figure 7 presents the timings associated with generating the referred events.  
Considering the specificity of multivalued input signals, which can be affected by noise during their acquisition, it is of paramount importance to intrinsically include an analysis of the signal evolution considering two levels of comparison, using a hysteresis strategy as proposed in [25], in order to improve the robustness to noise. With this in mind, two new sets  
Figure 6: The operational models associated with the events listed in Table 1 to be executed concurrently with the model specified by the designer: (**a**) Down event, (**b**) DownTrigger event, (**c**) UpOrDown event, (**d**) UpOrDownTrigger event, (**e**) UpDown event, (**f**) UpDownTrigger event, (**g**) DownUp event, and (**h**) DownUpTrigger event.  
Figure 7: First set of event types associated with multivalued signals and associated timing generation.  
of events are proposed as duplicates of the two sets referred to in the previous paragraph, where two levels of comparison (_k_1 and \(k\)2) are used to consider a hysteresis dependency. Timings associated with the generation of the referred events are presented in Figure 8.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Expression** \\ \hline \(Up(b,k)\) & \(b_{n-1}\leq k\wedge b_{n}>k\) \\ \(Down(b,k)\) & \(b_{n-1}>k\wedge b_{n}\leq k\) \\ \(UpOrDown(b,k)\) & \((b_{n-1}\leq k\wedge b_{n}>k)\vee(b_{n-1}>k\wedge b_{n}\leq k)\) \\ \(UpDown(b,k)\) & \(b_{m}\leq k\wedge b_{n-1}>k\wedge b_{n}\leq k\) with \(m<(n-1)\) \\ \(DownUp(b,k)\) & \(b_{m}>k\wedge b_{n-1}\leq k\wedge b_{n}>k\) with \(m<(n-1)\) \\ \(UpTrigger(b,k)\) & \(b_{n-1}\leq k\wedge b_{n}>k\) \\ \(DownTrigger(b,k)\) & if and while receptive transition is enabled and ready \\ \(UpOrDownTrigger(b,k)\) & if and while receptive transition is enabled and ready \\ \(UpDownTrigger(b,k)\) & \((b_{n-1}\leq k\wedge b_{n}>k)\vee(b_{n-1}>k\wedge b_{n}\leq k)\) \\ \(UpMonTrigger(b,k)\) & if and while receptive transition is enabled and ready \\ \(DownTrigger(b,k)\) & \(b_{m}\leq k\wedge b_{n-1}>k\wedge b_{n}\leq k\) with \(m<(n-1)\) \\ \(DownUpTrigger(b,k)\) & if and while receptive transition is enabled and ready \\ \(UpHyst(b,k1,k2)\) & \(b_{m}\leq k_{2}\wedge b_{n-1}\leq k_{1}\wedge b_{n}>k_{1}\) with \(m<n\) \\ \(DownInst(b,k1,k2)\) & \(b_{m}>k_{2}\wedge b_{n-1}>k_{1}\wedge b_{n}\leq k_{1}\) with \(m<n\)) \\ \(UpDownHist(b,k1,k2)\) & \(b_{m}\leq k_{2}\wedge b_{n-1}\leq k_{1}\wedge b_{n}\leq k_{2}\) with \(m<(n-1)\) \\ \(DownUpHyst(b,k1,k2)\) & \(b_{m}>k_{1}\wedge b_{n-1}\leq k_{2}\wedge b_Figure 9 illustrates the sets of the models associated with each of the events above, executed concurrently with the specification model where these events are employed. Similar to the previous presentation of Boolean signals, we also assume here that the \"Trigger\" events are associated with transition \(t3\).