It is expected that if you would like your temperature to remain within the range,

let's say minimum temperature or maximum temperature,

they're not in T max respectively,

that you will transition from on to off when the

temperature has reach the value T max and that you'll have

a transition from off

to on when the temperature has reach the threshold T min.

Now we can think about this logic as a finite state machine with two modes.

In such a model we could have two modes.

Q will be in the set of a state on, off.

This will define my capital Q for the finite state machine.

But now, transitions occur

when the following conditions hold.

We can think about V being the input to the machine equal to the temperature.

So, when the input to the machine is large or equal than T max,

and the current mode is on, then a transition

should occur, while when the input is less or equal than T min,

and the mode of operation corresponds to off,

another transition will occur.

The function L is the guard

function and now transitions can occur.

When that function has a particular sign,

we can actually say when

this function is less

or equal than zero,

and this is arbitrary, it could be larger or equal than zero or some other condition.

With that guard function now we can have a model of a finite state machine

that has a transition function that governs the evolution of the state.

It's output also depends on a function of the state.

And now the transitions occur when the function L,

which is the guard function,

satisfies this condition.

So now this model right here

which expands the previous model

which is known as pure finite state machines,

leads to another model of a finite state machine with guards.