1. Consider an event counter that is a simplified version of the counter in Section 3.1. It has an icon like this: EventCounter This actor starts with state i and upon arrival of an event at the input, increments the state and sends the new value to the output. Thus, e is a pure signal, and c has the form c: R + {absent} UN, assuming i E N. Suppose you are to use such an event counter in a weather station to count the number of times that a temperature rises above some threshold. Your task in this exercise is to generate a reasonable input signal e for the event counter. You will create several versions. For all versions, you will design a state machine whose input is a signal T: R + {absent}U Z that gives the current temperature (in degrees centigrade) once per hour. The output e: R + {absent, present} will be a pure signal that goes to an event counter. (a) For the first version, your state machine should simply produce a present out- put whenever the input is present and greater than 38 degrees. Otherwise, the output should be absent. (b) For the second version, your state machine should have hysteresis. Specifi- cally, it should produce a present output the first time the input is greater than 38 degrees, and subsequently, it should produce a present output anytime the input is greater than 38 degrees but has dropped below 36 degrees since the last time a present output was produced. (c) For the third version, your state machine should implement the same hystere- sis as in part (b), but also produce a present output at most once per day