Hello, in this lecture, I want to take multiple clouds a bit further, in addition to quite a bit that I covered in the previous lecture. Specifically, there is a new feature that is now added to 2012 that I'll cover in a bit. So in this slide, I'm just showing that they this sequence at voltage of zero if A is true, then at the very next near this voltage o'clock, one, B should be true. Now, if God's zero clock one are identical, that means they're in phase then this is similar to simply saying at positive clock zero is true. And then at at the at the very next step outage of proxy Ruby should be true. So again, From that, it implies that this particular sequence is the same as a sequence as shown in this diagram and age true on positive cross zero at the very next positive crop one or zero because they are identical B should be true and the property will pass.

Now, here these are the multiplex croc properties, remember that multiple clock properties are different from what typically clock sequences in sequence is again to rehash The only operators that are allowed between two clock domains are ombre lb, lb one and lb lb zero. So, in in the property in this case, we're saying that Paul's edge of clock 08 should be true. And at the very next bar, the proc one B should be true. That makes Since there is a non overlapping operator, so the clouds can be different on each side of the operator. But this is something here, I'm saying that pauses of zero is true, but with an overlapping operator at the next body clock when B should be true. So now think about it.

This used to be illegal in 2005 lRn. But now it's legal in 2012 LRE. What this really means is that add pauses of clock zero if A is true, and at the same time, if pauses have dropped, one also arrives, basically, they are identical crocs then B should be true also at the same time, that is true. So, this used to be an anomaly. But now what this particular property is saying that if the clocks are identical Then a and b should be true at the same posit, if they are not identical, then once a strong pauses are zero, that at the very next while they have clock one we should be true and that is identical to this particular property. So, in that sense this property now is a superset of this property, where they can be the same the clogs are in Cracow and can be the same identical in phase or they can be out of phase or skewed around the overlapping operators.

So, this is one thing I would want you to note this is now legal and this is something similar to what we have in sequence but without and overlapping operator basically similar to lb lb zero in seconds. Here cogs zero and cogs, zero on both sides. The operator. So, this is basically similar to clause zero a implies or labbing that is true at the same clock that makes sense. This is just a bit more using an OR operator in properties and here we are saying that it was eight o'clock one, if I was sorry, at budget of zero, if A is true, it implies non overlapping, that M clock should hold. And in the am clause, saying it causes your crop one either means through or at pauses of crop to cease true.

So we have Tunica called zero column one and column two, which are shown here. So if A is true at positive clock zero, then because this is an R, the property will look for b2b true at croc one. In this case, it is true and property will pass, it won't care for the next clock to because it's an R. But let's say B was not true here, then the property won't stop here, it will look for the very next clock to from clock zero not from cop one, it will look for the very next father of clock two from ground zero. And if see it's true that the property will pass, so just want to make sure how properties with three or four different crops work. And in this example, it's a pretty straightforward example what I'm saying is at top zero if A is true, then M Cloud should hold.

And M Cloud says that pauses are crop one we should be true and not have pauses of crop to see should be true. So I'm showing you three different clocks and using the operator and as well as not So as you can see, a clock zero is true. Okay. And remember, this is an end. So I pause the crawl one, which is right after clock 0.8 B is true, which is fine, but it's an ad. So he's going to continue to look for this part of the property.

And it says that ad policies are cropped to she should be false because there is a knot here. But in this case, I'm showing that she is true at the very next block positive block two from positive zeros is true so the property will fail. If C was false here, then the property will pass just to show that you can combine different conjunction operators with Mark multiple clocks. So very simple and short like that. lecture just a bit more on multiple clocks that I covered in the previous lecture. Thank you