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Hi, I dont understand how signal flows are to be interpreted. I suppose the concept is that of the sets in LO2? I also saw the answer to a previous question but it didn't help me. Let us take for example the exercise 6b) in the exam august 2019. 

  • a: 011 1111111
  • b: 000 0000000
  • c: 100 0000000
  • d: 001 0000000

We need to make a counter example of  [[[a SU b] WU c] SU d] <-> [[[a SU b] WU c] SU d] using these signal flows. I ll try to solve it please point out where my thoughts are wrong. 

Let's abbreviate q1<->a SU b , as b never holds our signal would be 000 0000000 meaning q1 never holds. 

q2<->q1 WU c as c holds at the first point of time q1 WU c is fulfilled and will stay true meaning our signal is 111 1111111

q3<-> q2 SU d, as d holds on 3 poitn of time and until that we only have ones , we have  q2 SU d  on the states before 3rd point of time, and after it is fulfilled because the third point of times satisfied q3, and we get our  signal 111 1111111?

Where is my mistake?

in * TF "Emb. Sys. and Rob." by (870 points)

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The top-down columns mark the same point in time, the left-right lines/rows the same variable/sub formula. The bigger block in this example is said to be repeated forever.

When evaluating a subformula at a position in the flow diagram, that means that we take this place (this x-axis) as “now” (t0).

About q1 ([a SU b]) you are right. We only have 1 from which on b follows after finite time, and a is present on the way there. Since we don't have b at all, q1 remains false.

About q2 ([q1 WU c]) you are not right. It is correct that q2 will become 1 where c is true, also it would become true on the way to where c is true (if q1 holds all the time on the way there), and (different from SU) q1 also holds where G q1 holds (place from which q1 is true forever). Thus, [q1 WU c] is only true in the first step. After that it is not, because we never see c again.

About q3 ([q2 SU d]) you are only partly right. It is correct that in the third step and on the way to the third step, the formula would be evaluated to 1 if we had d in the third step, and q2 on the way to it. However, from the fourth step on, the formula evaluates to false as d is not seen from there.

Where is your mistake? I think the mistake is that you do not isolate the time steps. As I said before, for every time step in the diagram, we consider this point as “now” and don't look back to the past for future operators. See also slide 9 in the exercise slides on exercise 8 (temporal logic).

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Ah ok I understood my mistake, I thought we could say the signal stays 1 after satisfying it once. The idea apparently is for each point of time to say whether a given formula holds. Thank you.

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