00:00
One process of on present one packet. Next. And those people who have their lives, okay, and they won't arrive. And then at the ground. So that's one thing. The other thing is that that's that's just state that this is a structure of the messenger. I'm going back and sticking kind of like it.

00:31
And if you assume that the mask is a message, IDs are incremental then state, the rest of the first message. For, if the Henry serial level there, the, you know, this is a higher, you know, higher number by message ID. So you're basically now we are trying the message ID with the order and this is excellent because it's going to make your life easier in the laboratory message IDs, then we have to order them as signs something else.

01:04
Okay. So anyways,

01:11
Just and so the next message can't be in a relief. So like the once there's a head of a message, there needs to be a tale of the same message before. There's a head of the message. I mean, I sent all my, my time messaging invited to back, and I've done it that then I start another message dividing away, So they cannot be on the same line and not Now they're actually having better in the problem, okay?

01:38
But I'm the same line and you have to stay back in each elevation, the definition of financial aid. No, this is just to set up the problem. Clearly. Yes. Do I have to move the the messages from? For example, one position in the way to the next position and federal park in the morning, the header arrives, his process at the low clock.

02:08
The next packet is process. So this symbolize the fact that is gap in time between them, they're coming in order, but in not in any synchronous way, or the arrival time is random, but usually we have to treat the this problem as an array. Why explain better? So can I draw on the ball?

02:46
So so we have to specify some kind of shift register. No, you don't have to separate us. No. Okay, so, for example, this is the first thing I'll get back. Oh, okay. So just keep yourself there. Yeah, everything you're going to specify is going to have to use a packets.

03:09
So if I did this pattern here because let's say that has a zero one, which says his body and has a value point is three seventy seven eighty six. That could be a thousand packets if you exactly on the Southern Buford lights. How do differentiate between them. Well, this particular package belongs to this particular message, and in this particular position, the next one, but we also reciprocate example is saying, with the network.

03:37
Look at that. The so we need to have some way to think about packets and being distinctive from each other. So you want to save packet When you think about what that is confidence. So one of the same one of the problems that should have patients should have a proper diabetes which should be no unique worldwide, just back and it does not exist.

04:09
We are creating it but we have to be able to to it has to be something that we can't create. So, for instance, I can have a formula, which is the initial position of the packet and scrambled. It was some encryption and give you a calculator. That's an example, or I can call the packets and make it.

04:35
You know how the line make the light number is the most significant digits and then one, two, three, four, five. All the way to finish. They import. The thing is that we can conceptually think of the packet eliminating and there's going to be terribly important. Because if you want to say that this package is different on this packet because ideas are you if you say that this guy is at the same it's because I decided.

05:05
Yes but why that is important. You messages are coming in different lines. Yeah. So that way you guarantee that they are not going to confuse packages. So this message is about going to come to the route or you are although I describable and then I'm going to pick up a ball like it was getting political.

05:28
Okay thank you have a ball. Like a bingo say it's an oh

05:34
Okay, so that's like in order to be able to talk about packets, you need to have a faculty now you can have other properties, okay? You can have the target message ID which is going to be very important. People say this packet looks at this question level is it and it's very easy to log.

05:52
Look at the header and design your. Everybody's same best. I mean, it's magical because I'm not seen that the router knows about what can happen. Then I have packet source that I can destination packet number maybe. Maybe we should have appeared like a number which is a, it's a first, the second.

06:15
The third and fourth percent. Now, some of you introduce so I normally find anything else that is definitely made us, right? Some of you talk about the message that lends That's a little bit. I mean that's a little bit questionable because message doesn't exist at itself is made out of patterns.

06:39
So anything, any property that you're going to talk about? And then I have to talk about properties of the packets. So so I'll be very careful about message concept in this. No. Some of you and added feedback location, this is 10 of them, these are all logical things that I can compute initially and I can logically think of being attached, you know, virtually to them.

07:13
This is change, this is really the essence of what the system is doing, is changing all the time. So you can't be a proper to other of the, of the people. The, I mean this, this can the fact that target has our location. It is time but the location is changing.

07:35
So it's not like this things, which are all constant, that can be carried with a message. So if you want to deal with locations, then you have a different kind of mechanism. For instance, you can introduce a we say location of the people and then you define what location of peers.

07:58
The problem is some of you have defined that location and being a pair of IJ body to use a different name for input and a definite pronoun. He should. It should give you a triple. Not a fair. It has to tell me, which of the a test and what coordinates that array.

08:20
I mean, in my case, my solution, since I use the same array location is a pair of IJ and this is going to be fine, but magical correctly. Which means that, you know, there's really no vocational theme is that I adjust that, you know, let's say if I use the only one, the one matrix what makes me major so by J.

08:46
Equal B. So this will be turned IJ subset to making somebody. Now there's a company. Another vision of complication is that message the packet or something. And as much as you suspicious,

09:09
Some basically says it's here, if you use 2 different arrays, you have to use a correct name and then you can turn the eternity. Both are they named high energy But the other thing is that the packet could be inside the router. So you need to have a mechanism to say that it's inside their own.

09:30
So one of you, one of the teams basically said fagot is, if I can't find it on the on the input and I can't find another network. Then it's in the route. I think it's would be with the better to basically introduce some notation leave. And let's say he for example locations, the former patients and this is a set.

09:57
It includes all this on this possibility. Here. Union, not say a little louder and more.

10:12
So vocational P would be, let's say I enjoyed the location in space or would be wrong to indicate that it's not on any locations in space. It's inside the rock. Okay? So this, this is going to be very important concepts. And as a concept that you may want to think about is order a is, before being packet.

10:37
One is get too. So for instance, for happy is probably here, you know, it's really if between two bags and his hand over different ID, that's an ID. Then this one says the same message I did this. I don't online one way to express property. So location is going to be important and maybe ordered think about it.

11:10
So I made my solution. I basically something like this and I said, it's one is in front. It's behind like two in behind. I'll use that location, but you don't have to use that. I'm just saying that this are important concept, they're not part of the packet description, okay?

11:31
This sort of different concepts that you have in, and they order for the other companies, like with an index. Well, don't get number one to lose, right? I put it in which you may need, it may not need it. Because the fact that I use can do it, Okay.

12:08
All right. So here's the way done. Necessary is enough to identify all adjectives, even that they are scrambled all of them belong, but you can take two packets of trying to say message and put them like this. It's not the same messaging of, but the old number and the router uses a message ID, but we specify us outside because we I mean, we use a message.

12:40
I mean, but that's not enough to be these things that packets and we have to make it back is what unique and soft version. So, it can tell the torn different, because they look exactly was wishing. Please a loaded ovation of eggs, IGA. Yeah, this is your relating, the input at the output of the package.

13:00
Well, I have a matrix here with zero zero here. So, I call these matrix taxes here, so that cannot be to equal or outward, and it's greater than n. Plus 1 is equals on this greater than 10. I know that is out. It is smaller than 0. I know that same so I can define those functions.

13:29
Very, very easy. Oh, so this gravel is in that. Make. Yeah, okay. Now what's going to happen operational. So any more questions about it this and this this is really important to set up the stage so you can talk about it because you know, you don'tify the location properly.

13:49
I mean nothing is going to work. Yes, what

13:55
The faculty is universal, there's no two packages. The same idea in the terror. I work I can number you know the theater is always one and the first fact that the body of knowledge. All right? No, I want to help you shape up the sections, but just make sure that we understand what's going to happen.

14:21
That that obligation is that they input has behalf, that will be able to operate now divisions are wrong and it's important to separate those three cents because of, you know, the location of the evident couples had assumptions about the world outside of congregation of the router had requirements on the electronics of the government, to their different.

14:44
So just saying that, you know, this package is going to get from here to there is not a good way to specify the requirements because now you are mixing the environment and the in the program that you write all into one single soup. So you know, you're not really giving any clarification for me as a designer of the rotor what I should do.

15:08
So On the environment, we need for this to to make sure that it doesn't stop feeding the data that's obligation on the evils, keep on sending guidance as long as you have them if it's the 90s emptiness, no problem. But if there are cactus to be sent, please send them.

15:29
So what does it mean? Is it in Spanish? Have to be, there's a space employee, they should move. So eventually the first bank that gets and they turned over into each other and all those problems, right? So there's obligation on the input feet, do not stop because if you stop, then the doctor is on the normation.

15:53
So we have assumed that they need for this computer, feeling better On the output. We have to assume that the output continuously the device that is reading the, on the cable, it always consumes the data, it doesn't block the router. Because if this device here leaves the packet in that location, some sort of buff the project is not fully there, but the next time.

16:19
So that's a property of this as inclusion office. The property of, I mean, obligation on the environment or the output environment, how could environment must consume the data, which means that if something is here, it should be moving up. Would be. And then next room for the next package, if it doesn't behave like that don't explain the proud of the behavior profit.

16:47
So now it's like basically then you have to have a section on the sanctions about and which is the equivalent of and that and then and that's your money for to the doctor at home. It only should be what that expecting them to do in order. For example, then there would be assumptions about, you know, and they should be, you know, these are the foundation, of course, I mean some of the idea of using leads to and until in places that doesn't really make any sense.

17:28
But, you know, here they have some someone until because he promised when you do the initialization, see how we speak to properties of the progress. So, you want something the to and then it will be properties of the

18:01
Of the. But in other words, fun if there's an input here, it better. Not be even any input has some stuff eventually put it out, so that's not application of the route. Again is a progress condition.

18:30
So these are provients on these two program fields. Again here's progress which is the ideal or could.

18:49
So with this obligation, if we basically look around like to take it back and deliver it out, we saw a 90% of the problem input lines processors on the even lines. Feed packets.

19:21
When it doesn't do, it doesn't assure that after behaviors correctly. He just make sure the whole pipeline works that doesn't say that you want correctly and that's where you need to start thinking about how the properties.

19:40
Mostly going to be in guidance, which are properties of the inputs, and the offers particular values, the relational, the packets, and the glaciers in packets and where they are located and who ordered these things like now. So there is a way to an invalid, it's a something to initially, right?

20:02
So that means that if I take a snapshot in the middle of processing, then that should be true. So for so many of the properties that listed in more than evaluating basically says, you know, in there are two messages on the opposite. They come from the same and of, I didn't know, express modeling, you know, you know how to express the same source.

20:24
So they mean packages are both on this and packets are both of this output line. Say, come from the same source implies that blah blah and there's something to do the order image there.

20:42
Messages of an alphabet. I know it mixed up. So some of you really try to specify properties like that by saying that if you are in this order here, we're going to be in 10. More drama there from was there until you are here until you are there. That's my family.

21:02
That's not true. You're going to recycle their water, so you're not here anymore. So the unless part doesn't it doesn't so basically had to look at. That's why we describe all of this. So then we check our outputs, did not put satisfying to the proper properties.

21:29
Yes when you with these crumbles? Yes once right? I think when they are router and packages, it puts them in in a slot of the router picks up packages from the input and keeping up taking up one or ten that we don't know or not because of designing is not or we don't do the design, just tell what a good router should do.

21:58
So, if you pick up, you know, one bunch of packets store them in its memory, going to two days and then start delivering it and maybe even online one first and the line, man. And then we do them, they might assume. You know, it's in my don't do it, you don't we don't control how the router works.

22:20
We only control. What a good router is allowed to do about to drop packets. What if I packets or change the order with Nintendo order of the first message from, like one arrived, you should let can be stored inside and then the second message, arise shouldn't allow the second base for God first.

22:51
And the way we tell that is by looking at properties.

23:00
This song. So how does the output consume the packets? What is empty? You put a packet and it's moves in the line. So it's one packet at a time or one, or one. Message at a time messages doesn't really exist. It's all made out of packets. Oh, okay, so one packet of the time.

23:30
Oh, so you know, if you see the packet here is to move it for about in that packet in front of, you know, and then remove those clothes, my grandfather and then move. That's why it's a non teal. Oh, okay.

23:52
What is into saying? Like it will practice exists and the input, then that leads to it's too unique, but a couple of promises just too high level. Okay, well, good night aspect like that but it's way to high level. It doesn't say anything about. What how the router has to handle the percentages?

24:15
That's why video is just to it's like you want to set for a assumptions about the input process or output. You would like the subject of our code lines and then specification of what the doctor does. And that also doesn't see the implied story sees the last element so you can only tell.

24:40
Is there something there? Or not because there's a communication problem have the product here and message in the buffer or not but it's not that no one has something. And of course I mean I'm emphasizing the fact that arbitrary delays which can be but in reality it's an alternate work at 90 second speeds.

25:05
So now what new city does get, whether still we don't have emotional time. So we have to use the notion of random we simulate entrepreneurs and impressive, arrival time. We send was similar on terms of consumer powerful time and signal and marketing. In terms of how long the router it takes to process things and ordering processes.

25:38
So the message ID exists by itself, we don't have to design that message exists in the head of only oh, we propagated to everybody else. Oh, because we know if I know the message from the input line, I know the message. ID for this packet. I can I cannot associate with become modify himself.

26:07
Oh visible. To say that we know that. Oh, on the but we have to decide the ID. No, you're just a says unique. That's all just need to say, you need. Need order on the same. The same input then you could do that. I think that's just saying. If you need, it's probably holding it evening system.

26:41
And you don't have to explain. I mean, if you kill, if you could not generate an unique idea in a larger number, there would be a problem. But you know that these steps people have equation. Yeah, even one is has already been forwarded to the whole political Queen Creek interview then because the other message is already this, and we needed to measure that no more remaining in messages on from that target from that message.

27:16
Oh yeah, because the message could be only could you order behind the So, no matter where it is, you should still give yourself proposal to specify the correct hardware. How do you alone that that a message has already been recently? It has a tail, It's a tail hasn't showed up.

27:46
Clearly. It's not finished call. I mean the router picks up the header and it has to put ahead and out first nor the body and has to put the next body first to next until and put the tail last. It has to make it keep the order of the message, and that's part of the properties.

28:12
If you want from this counter, we want this now to maintain the order of the packets in the message and we specify that by looking at the output and say, yes, you are doing it, you know, you're normally oh that header and the tail is for the matter. Lot of the package it's for the message.

28:29
Okay, magic is broken up. You want to six packets is a petabyte which has this one. One and source of destinations is a body which has a zero one load and as a tail which might be one zero and nothing. I mean that would be a little bit taller but not such one target at a time, not a message.

28:58
So the method the pack is, the message could be distributed on inputs inside an hour and that's not what, okay? Any other questions? Yeah. So can we specify that the water holds some variables? Some states. The only state of the round is that it holds. It is some packets that are inside the ground.

29:29
Or some packets. But can we start at this package is coming from which input line is. Look at the message. So you see, you know, oh, we recommended the pack additional tags that are force, specification. Only cannot be used by the ground. So we only need wider packages inside the router.

30:07
So when you talk about locations and locations, we're back at the input on the in the algorithm now and then you can compare locations between the different. So, like, one property for him, says that he forgot his on the output, and his characters having destination, and it has to be an outfit on ever.

30:35
It's kind of another half. Even packet has source one. It has to be online. One can be anyone else? Those are you guardians properties that we specify their integrity of the system and started the simple things. I mean few if you start putting strong formats about location and you don't have performance cells back, it is on one location first.

31:09
Then you confuse because yes this. What do you mean that location of a little? Disparate could be in five different places. So now he might leave his stated that we can only on our location. Then when you have a farmer, gives you the location that makes sense. But if you don't stay that, it doesn't make any sense.

31:32
I mean, So the ordering presents, that's always interesting that the sanctions of all the behavior of this component, then, you know, the properties of the content and then all the constraints which are really the invited strategy. The correctness criteria for the quality.

32:04
So make sure you have a picture and it shows, you know, some messages and they help the messages different, you know, shows they have between them the packets and the second picture the type as you just have a picture like this. So I always spend some point in the real time on this but this is your last homework.

32:48
The greatest gonna. So it was specified that a perky only has a one location at a time. Do we need to use time time? That doesn't exist. But how then how do we right? I'll give you a symbol and depending on the symbol for me.

33:15
Whatever symbol mean.

33:21
Exist. Yes. Exist. What? But I'm not sure about the. Well that doesn't part that's a part of the importance. Oh if you need words or something? Yeah, so you need I J such that. Hence I J is equal to P for all of or maybe pocket. There's an unique location and this that what?

33:52
The contact just or I mean, Location of

34:09
Okay, by the time, what's wrong about this is, it doesn't consider there about

34:18
So, it has so basically,

34:27
Is any text like that from location of fee is x. Our x can be by j or x in yonder or the draw equivalent.

34:43
I'm going to use a proper and what, anyway, you unique location. And your dad is there and he's got him but the location changes but there is only one ever in any state. There's only one place where the package resides that all says oh, it doesn't say it's application 33.

35:08
It says, there is a location for this state is 45, or that. Next state is 110 that exists. It doesn't say this one says that exist one or. So with, we don't need to specify point in time,

35:34
But, you know, coming up into proper. Proper the definitions are popular. I mean what's a difference department locations? Makes it easier for more complicated and don't offer. Go overboard with respite in which definition see when you use it. Because I've seen situation when it defines you that you never use.

36:05
And as a way to express, the same thing as the number of places where P exists is one. Oh, it's another word like oh, and bracket in common especially it should or

36:26
All right, my friends and neighbors.

36:32
Remember, the problem?

36:45
The master. 0.

37:00
Right? And this would be what's left of the range, someone who are. And then, we have to get a number of

37:13
To just add things together to the level of. So. And then we had a number of properties and I'm going to revive them, right then. Again, I've only been for one of the, for one of the programs. So we have the program hard in the program. See is the program our home growth and all I see for help see was processing season this connection with those present.

37:41
And you can look at R, we had the value as people say mother gray.

37:59
So the sum the dad, everything in the in the way, you know that in some other change then he had true needs to. I make one which means it's already becomes one. We use only the of course it always is one zero. There's a little bit website is the first first month.

38:43
And has a variant.

38:51
And by,

38:57
And then we had that insurance idea on the x and shows. I spawned index or I using performance and then so since again, yeah, this was like this one doesn't mean by pi, but you can select this. So one is correspond to this location. So this location here, things going to add this that I'm going to zero it and that's going to reduce the time.

39:43
So it's guaranteed I can point my thing around this statement that is going to do it. The wonder is I might as well.

39:58
1. So once we are here, there is no, there is no, don't want anything. Take this and zero down because it's not stable and then which is highly one inside. Okay.

40:30
Okay. It says, if you have anything advisable to one, you've got to say all the guys in here, then give you the entire value of and for seeing is really very similar that we use J instead of

40:53
Remember this. Okay, so we wanted to basically stop looking at properties of what happened when you think are and see, if you guys see what's happening, this is moving in this direction. This is moving that direction. Eventually we just one said that there was one zero one because and that's what the behavior that makes me just put everything together.

41:27
But we like to be able to prove companies of union by using properties of the component and that's just something that's necessary. Because, for instance, and I wanted to prove that as

41:50
J.

41:59
So basically, this has that

42:09
So, we have a group of places instead of in a properties and variant in one and stay with the other, then you can conclude by hand posts. So it is an invalid. It's not. It's also evaluating C, but I don't care if we don't have to care about the fact that it's not even only to pick up.

42:33
We can pick up, just a stability party. If you say, this is a dividend that sees local statements. So here, when you go in the market, they stability down the program. Therefore, they've got and survives the union and their first. That should they? Okay. So, so you have any value one in from that one, and very brilliant by two programming for this.

43:14
Now, so this is invalidating, see if it's also stable.

43:26
So now we have stability here in the garden. There's want to combine the programs that are and see that this environment because compared to the beginning of we gotta put theorem that state into that. Anybody says because well this cannot violate it and this is initially true and cannot violate it.

43:52
Therefore has to be true for the combination but particularly that one supple thing under the table is the fact that we could not put this to programs together. If that initializations incompetent so we were actually implicitly taking advantage of on that question here.

44:41
So we want proof that once the whole thing that used to a corner that stays there doesn't change, some means that everything you see will accept those is called. So you know, I won says that everything below this, zero J1 says the right of this is 0. Therefore, So the proof something like that, you can start focusing on targets table, you can see.

45:19
So, this cannot be modified.

45:32
And is moving this after the left, quite the key issues that all the numbers are possible. So he can, he can't come in, makes this whole zeros and therefore, jump high up. I is famous more my only this little column on zero can run. This is just something to the left, because the knowledge, so this can only increase.

46:07
And So the statement see, then j equal.

46:19
Why?

46:23
So you change the particular thing, you know, this can and basically and music we're not into opport the worst case, suppose number. So the so in order that two table in most most. And so they, that's there before actually for everything. And I also. So then we can combine the

47:10
So I can understand when C.

47:17
Type 1.

47:29
Property here. Who says?

47:35
And then you provide the two.

47:42
Of J and then I'm on entertainment escape.

47:57
I'm gonna give you one more problem in the tool bit. We can prove something badly, J, Cole War.

48:22
So again, we take advantage of the business stability and the evidence in the property because you see this is true in both of them. So the combination. So since I was 0 to the left then 0 below then acid, only see that it's not 0. So it has to be 1, is once there is no 0.

48:51
So it has the proof is very much the same, okay? Any values just combine the guys just ability. You think that interest ability to

49:07
To do something different to

49:19
Obviously writers are not like J is our metric For practice so you can decrease the network as it might decreasing the higher level because you change but you can't depend over them. That one more people very either variant here. That's Hi. Jay have to be in the most valuable one.

49:43
You like to hear from another crime organization, so

49:55
The way we do the proof, I collects shoes last. Born came knows another text stem.

50:32
So, remember to combine the stability was ensures ensure can survive. So this part has to be stable in the other program in order for because sure is to fast and that's and they just think that. That's so basically we're saying in this program for the mark there's a standard equalization.

50:59
The reason we have to make sure is that as a program is what I'm reminding you by making this. So this is stabling out of the program as a program to standards that for our children are destroyed. So it's going to continue to be there until the point where we choose this particular statement.

51:20
So then from that we basically flying wax ensures my strong one.

51:35
And again, do the same thing for J. Taking my wife, Japan wine was

51:47
See, the improved and the other one. And so the next thing we want we do, we're going to using induction and we're going to basically show the device equal to x. Thanks to Isaac one more. False hard. See and similarly Jake and why these two calls in see?

52:30
So, the next level. So this is proven by industries.

52:40
So that the last step we need to to take a different take advantage that the fact that iPhone 1 is stable and taking one stable and so we're already proven before that. I want on this phones in our box setting the same as definition of statement, right? And J equal 1, unless

53:17
Can't see. And so one is we do, that is a completion CRM that allows us now to

53:33
Basically combine this properties here. So we have I Jane next. Why makes the and change? Or false.

53:57
And this is our there's to be.

54:12
The one you want to see the completion therapy process?

55:07
So you see I just run and this is all and we're all bi for our. All right? Well, this is our PI small thing that has high correlates and shape or why request.

55:30
Then for this part we have why for July Q1 is Q2 so we can combine those. So we so we have 5 j.11 so we have this false like proven that here so we have. So we, so then we can have this, which is that for B sports there.

56:06
That's all we carry the PR and that's the point. So that we have something else on this four lines. This is that and that's a way people who really are digging to the unity. That's a way they work. They know these formulas by high and the 25. There companies be able to look at questions.

56:42
Okay. One. One issue. Not because it we assume that their name was positive. Either that positive or positive Then we hope we don't get a stability of. So the numbers for the added out and they get even positive numbers could give us. So the formula guess is no longer valid.

57:11
So we need to modify this formula. The other thing is, and the typical way to say eyes, one of them are equal to x. Sure. The time he stick. So there's one thing doesn't complication. He said this sum.

57:35
So now I enjoy actually outside of the makers. So we just have to release think of how we define INJ in the case, where the sample is 0. And in this case we announced the so we can handle it but the definition of the change.

58:00
So what have we done so far? Basically introduce a concept of union with a two programs which are not incompatible with each other and also with the architect because of decoration that appearances the same way and initializing the same way we take them and put them together and you're getting new program by just mixing good lines together with boxes and then we can take properties of the individual products.

58:26
So one of the already done and you steer it to propagate some of the sport to the physical microphone, not everything propagates developed generally we need stability working guidance. Okay, practice properties.

58:49
Now, this is not the only way that we can can do create composition.

59:01
The next is considered a difference between conform.

59:20
So remember, this was called Union because here you can union assets kind of sexual position

59:42
Okay. Now is a thousand comes from concept of composition is super

59:57
And has this. There's two forms organization and

1:00:16
So, what is idea? Have a program and you well, let's think you're going to actually. Next time have a program two bunch of products running and we want to find out to build terminated. So what do you do any system, good system, or you run a protocol and that protocol runs to check on the programs and one very important principle of running that protocol?

1:00:50
I mean the protocol system completes will tell us. Yes. Everybody's finished. Okay. And part, of course, remote complete until Christ, fine. But one of the important thing about the protocol is that it does not interfere with the computation, it doesn't force things to terminate. Okay. So super position is a form of composition, where you take something and you aren't really stuff, but this stuff that you add cannot affect what this original program is that's called super position.

1:01:28
Where superposing addition. So, for the simple way, the simple way to think about it Joseph augmentation. You have some statement in the program and you want to do a proof that the statement will never be executed more than 10 times. Well, if the statements just in the stimulus of any guards, we conf because I'm going to be, so you can say yes, if God G.

1:02:03
So that's a statement in the underlying program we can augment it on the statement, a quality of k plus 1. If g. So now what that means, every time has a successfully, what? Every time is selected successfully, executed. We implement the complicate Recognize doesn't do anything to the program that no damage but now we can use this conference in a proper call, so that's what augmentation.

1:02:50
And before painting of this famous system as a matter. And here's the person who, okay, plus 1 just things you're understanding. So these augmentations are inside the program this week. So, we take the text of the program and literally we use red color and we add things to the text.

1:03:26
I mean, that's the best way to think, kind of code is black the original text and here is red. Seems that you have and everything. We have to modify the original black, any property of the black text still there. But without touching anybody don't modify the state, it is not the monetary system on the internet.

1:03:49
If track and analy.

1:03:57
Back, it doesn't insert packets doesn't really impact it, it just monitors. And then space was used to determine detective and intrusion for whatever else you may be happening. That's exactly what that's why it's called super. I mean, let this thing running and we are just keeping the camera and pop little bit.

1:04:22
I've seen me if I want to find out how many times is, was selected, which in this meeting is because I said anything about Christ, I dropped it. The guard again, I encounter in Texas. I said this meaningless and I think we can do is basically, we can always demon often.

1:04:50
So, how far is just now. In addition, remember, this is using using a red soap box, you know? We had alfine red. It's a new statement. We have to make sure that alpha has no modified any variables in the program CC alpha. And if it's here or there it can breathe, any steady information.

1:05:17
Okay, look at any variables but give up modifies since you cannot modify the state, you can't interfere with

1:05:31
When you add these augmentations, do you have to add them in later? Like the declared section like this if this k is added of the case, will be the player and pay his musicians. So yes they are. That parts of augmentation. See that you have to do it in the in these states in the even knowledge, but the basic and that I just kind of obscenely stuff.

1:06:08
The basics thing is that he's a synchronized state and his statement here for that is and from earth you had one of the two into forms. So, once called organization, the Disney is union is because very restricted from modifying, the variables on and only 25 your own veins, you can read anything but you never modify

1:06:40
So you might do these, for instance, just simply by the proof. In some sense, was adding all the things just to form a lot.

1:06:55
Added extra variables in therapy so it's not any, it's a variables but don't exist. But the evening is part of our protocol, which is basically checking the router has been. So most of the time one is sometimes group. Imagine this is vagos and then you can do different improve space on that properties variables.

1:07:29
And sometimes, in most often you,

1:07:37
The money to the computation to bring dinner and replace our properties in the combination to do something. That's,

1:07:53
And computational flame.

1:07:57
Any questions and anybody said remember using just to so that red color to see them original programs, any program, and make sure that on the side, sign side of this statement that not variables, that will not believe no available different.

1:08:24
Okay. Now, there's another concept that I like to, to introduce and that's mistakenly then.

1:09:15
To love that. But there's one of the third and it wasn't there. I think it was furniture.

1:13:18
All right.

1:13:45
And they have many tests. Yes of fantastic.

1:13:55
Anybody has actually tests kind of stuff another, you do have so you haven't finally exhausted. Yeah, how many courses?

1:14:27
Type 1 here you yeah.

1:15:27
You know.

1:15:39
Health is going to get my face about five minutes.

1:15:45
You know, is that many of them?

1:15:52
And,

1:15:56
See.

1:16:07
Amazing.

1:16:36
Okay, so this constantly won't be conditional.

1:16:52
So can weigh the term suggested that this is is a property. That's true. Based on some ass and it's always like that. So well. So in my group, we took on the challenge of proving the mobile IP protocol and which mobility but we needed to realize. It don't know about these the program work only if you made the second reason with assumptions which follow the listening, 90% of the time and 99% of our country, their own truth.

1:17:35
But mathematically, the protocol doesn't believe guaranteed and that places verification responded. So one to use conditional properties. Well, one is when you want. You want to? We have a component. If you have properties of this component, it is component. Interacts with as a if you don't have those contact so you have to make assumptions of what they might be doing and then you prove this component.

1:18:05
Correct based on assumptions about what they're doing, another way to look at it is that I divide designing this component and it's proper depends on the environment. Behaving a particular way, think barium doesn't environment doesn't have the way specified. No guarantee is much important. So if I build the, you know, transformer that works for 110 and you put in the 220 outlet in Europe, it's gonna run.

1:18:39
I mean, I, you can't sue me for that, right? I gave you the spec. I said this are the inter. So if you look at the problem that you that you're talking at the beginning of the class, there are the router is going to work properly only under the conference that the processes that they will that feed their will consume the packets.

1:19:05
Also. So it's a point, it's not. I mean there are those that in some sense what we're going to actually have the color of the router improve the code that I some based on application, we need to make assumption that. The environment is not being something bad, so he's not providing us to head of one of the necessaries wanted to another want to tell about another or not dropping tales and those are not expect me because process of specific property in most Italian them.

1:19:43
Now, you can say, well, okay, we can put the extra conditions in since like that but of checking the best things. Yes, we could do all of that to create. This is the router more robust, but now you're slowing down throughout and you find it to work that 20 nanosecond rate.

1:20:02
All those things are basically going down So I don't want to put them there. Another situation is we have reactive systems. They environment is treating us there. Well, based on how the, what they think, how they can put that environment, you may behave in different individuals. So again you can improve the system works according to spec, honored assumptions, the environment satisfies said the properties.

1:20:37
So basically what we're going to do, we are going to have is something like this. We have.

1:20:48
You know, population.

1:20:54
And I promise this is any kind of it's going to be properties.

1:21:03
If you have two products and FMGF g have box g and then we're getting properties.

1:21:26
So this other assumptions have been forgiven, These are things that basically we if we can then can include for free them.

1:21:46
So general, what happens?

1:22:00
One of these components, it's kind of has any of the test and one of the components from

1:22:17
So basically, you know, we have dealing with properties of the composite based on this generic thing that it's outside of and we don't have a textbook. We only know you want, you can make assumptions about it. So let's take some example. So, let's say the processes. Okay, table.

1:22:48
And we have why people, okay?

1:22:58
Have and what are human to us? Is that we know that we have another text and another ingrown.

1:23:11
Why?

1:23:18
So we know that every man's why? We know that G. That's not decrement. So, we can use this hypothesis, this information. Now, prove the conver so you still use the consumption about the environment. Text of the program your access to, to grow. The cook is in the what? So they left, they last sentences in.

1:24:10
So we know, we are standing around physically, we have a standard, I mean, in the south of the she is not going to put it down. So based on that conversation too. Then we can compute the eventually guarantee the wise level. We're going to go.

1:24:34
So generally what you do is when you have so you have

1:24:46
You know, Q think that's more objective, is what you're going to do, all the conditional properties.

1:25:10
Fee and using as inferences.

1:25:18
So, the property that is given is conditional. It becomes a difference for basically particular doing put the hypothesis and then you automatically get conclusion. Now, he's a probably Q is also traditional then. So now you is a part of this inclusion in what you need to do. You think age moving to P.

1:25:52
And then you think see decided to keep they can assume that each part but then you have to feel

1:26:11
All right, this also a group we have started. Let's let's get some of the concrete for great example. So, let's assume that we have, you know, like we had to the programs that I am, I see. So, let's let's listen to the whole program which was not AX. And we do this before, we take this we something about enthusiasm, right?

1:26:48
That's exactly what we did before. Just now him living it away. So and we have all the properties as before. It's again, it's just to the current and the color making one symbol. So,

1:27:16
What we'd like to prove. So we have this problem here can have and very environment.

1:27:34
And we basically what we're going to see that he wasn't what we just explained, okay? Thank you chooses a location and the previous cell and zeros appears. Okay. That's a way people. Now e is another program could kind of does the same thing, but can do anything that we don't even know about before.

1:28:03
It says, you know, maybe there is a they just sell here.

1:28:13
City and seven and eat besides the sauce and some So basically it's an environment that can help us speed up. The execution made do other things but had to make sure that he doesn't really seem that the damage what we're actually trying to accomplish. So so basically we want to know there's a properties of this one to put this for products together that we desire, but those properties should be conditional either.

1:28:50
We don't have access to the code having something satisfying satisfactions. So, what we want to do would like to pro True. This to this one equals s debugs together. This is the sound of all the values. X1 is the location. Always the left for a moment. We right. And to prove that this is happening for you to the deferred act together.

1:29:26
And we also want to prove that this table

1:29:41
So this is what we want to prove of the combination of the truth. Now we have that expertise we can produce properties of peak but we don't have the text from 8. So we have to basically make our conditional. So this is on some hypothesis and whatever I will do now is so we can say that we needs invariant.

1:30:24
So what did you say is it? We assumed that E does not. That's not destroyed the environment that came early. So if we take the original sound of all the values, it's always the same song. He is, no, he can do something like this. So obviously still it could do something like four and six.

1:30:51
You motivated once like that but you would overall sound it's not change as it is a consumption. The thing is that is this assumption enough.

1:31:07
So if you think about this list of conditions, basically says, you start with, I being and what this is Jaya and they moves to the left. So that's the left, eventually becomes one. That's what basically it's saying, and when it becomes one, all the sound is already in that particular cell, okay?

1:31:35
So, in program p,

1:31:42
We have at some point is value of J here and everybody else is here, right program, E could take a value from here and move it in there. So now Jay jumps back so he no way you can prove a property, like this is probably this property is going to prove as an insurers said, I'm going to point on the statement and confusing them.

1:32:14
You are going to you know decrease the nets, quite of this. What is could do? Could interfere with a metric basically, is that a long as we to decrease it? The longer. So I could do that whatever and forever. So then we can never prove this property. Can't never be possibly for this company.

1:32:42
Here isn't because it could take forces of a number and moved it backwards. So this is not not sufficient, it is weak to what we could do is basically stable

1:33:14
So people have the stability of zer that means from that, it can also conclude the stability of J. Says, he's Jay stability. Me. And you know, it's subject to ensure here. Then we can put the insurers of the combine. The combiner products questions.

1:33:53
Think in our daily environment is the input. Yeah, they even end up because after this, we consume the first cells in order for their algebra to put in for the dialogue.

1:34:10
And but I mean, we are we are not separate. I mean, we're, I mean, we're not even compared to this vacation, but we want to separate the pieces. Specificating such a way that we can think about input, think about outputs and things about the router separately. Not as one on.

1:34:31
But we have to drive our homework this way so you don't have to stay because you're writing us, it's not the conditions. I mean, you could have written in this way, but but I think that we better to make the problem to make a problem manager so you can actually solve it.

1:34:52
I do two things. One, I basically said look you got to have this array with all future names. That's supervising someone. Because not can refer to the actually the emails to basically locate one specification. We evaluated the modular colorway or to create a specification for the entire system, including the assumptions of all, the environment about the environment.

1:35:22
Well, I'd like those formula separate, but it's all one single specifically. So, yes. So those are the two things that make your magic.

1:35:38
But I really have to do in a real in a kind of more realistic. Way would have to introduce little toughest thing about art as being a reactive system, and we'd have to sing about the environment. So they have to do is basically something. Work is a router. R environment we want to to and then specify what our cause under the assumptions, about the environment.

1:36:20
But because you form also did a lot more that I was complicated. Now, both of the things that so you can see them motivation. Why we need to make some some assumptions about the environment in order partly through them together for what the with it, for example, many angles and each input is an environment for all the energy that is every second that is a

1:37:08
But worrying, the inputs are different devices. For example, a satellite or it doesn't matter. Then they're just it does matter then they have to have additional additional information somebody from different devices the package later differently. Yeah. Sometimes I don't know. Thank you now. So different information and running different.

1:37:36
Protocols so far, this has a router. May not be a normal actually process. The new message until it sends back a message or we some sort of requested a certificate and that that our acknowledgment was, in fact, there can be a lot of population.

1:37:59
So the union has a preposition and important very important ways to think about it is clinician about particularly as they apply them to the labor.

1:38:16
Can we ask yourself?

1:38:36
Thank you for partners. What are going on?

1:39:00
So,

1:39:06
We're going to have a device on the filter.

1:39:15
And my filter does it filters out lesson. So the messages are coming into the filter on four days, I've done automatic filter and for the and the filter has set of consonants x

1:39:41
Inside part of a specification. So really, I feel there is about it. It's filter. A big in with a I'll be in constant exercise. That's a way to characterize. I feel what is what does it do? What depends on one axis. So let's say that x is a set Tuesday and any message that is divisible by 2 or 3 is.

1:40:21
So you can get a seven here. I'm gonna see a cylinder. We had a six. Here we normally see the six. Forget, that ain't here. No, you can get.

1:40:38
Okay.

1:40:42
So for what you wanted to do, this is basically make a program and works like this. It's probably the rise by a VNX. So you think of those is the animals to the program and then write this specification, a genetic transportation for the children in corresponds to this behavior.

1:41:14
Now, the reason you should try to program first is because of giving you the keys on your side in how they feel my pork, but I can't really understand questions.

1:41:40
You know? Hey, it's important.

1:41:48
Well, you can two days ago, you just copy it and come get the value of zero and the very request. So, to access A lazy. Do you say a colony called?

1:42:08
0, something. And, and

1:42:18
W. That kind quite hopefully. Yes. Do you assume that it's an input? Is altered out? It just here. Drop it back.

1:42:49
It's featuring. What if they said right? Well, access and the filtering constable anything that it is more like two or three is drug. Oh, this is six was drop because it is actually three able problem, because this is one, two, 15 was best through because of my reasonable way towards me.

1:43:41
Bad program, That is even harder than 13, right? Or something current to be the difference between The writer code.

1:44:00
Help. Put it.

1:44:06
Clear? Because it could be a little bit. It was pretty good. All right. Yeah.

1:44:51
Was no wonder.

1:44:59
Is the set of x a financial or a good. So it's always too.

1:45:13
So, A B and X are coming to the US argument of the part of our fame. We need to understand what we have. Tables. Behold their shares of this world. All elements and access team. I'm gonna skip this. People started working initial here. Is that?

1:46:00
Yeah, that's the main way everyone. So, the initially

1:46:12
Completely.

1:46:23
One.

1:46:36
Engagement. I'm not married know everybody moves.

1:46:45
Very long, an hour back, believe it or not. For the cont and we can defeat a little bit, right? We're out for this event. I'm doing about the spec first of this, It's important to get this device.

1:47:25
It's available.

1:47:32
Well, I guess we could do that in Australia. Just a second said, I actually said that. Hey my name. So that one's a little problem was what you just did.

1:48:15
You know, the numbers and the main reasons. So, think of the protocol, he's environmentally. Ok, he has to actually.

1:48:43
Yeah, really shoes. Are three three here you can. You can post them with the in of be ready days from the robot. Say, hey comedy, first case.

1:49:19
If you have anyone. Yes, sir was disenvised.

1:49:45
A, and B over here, point, in the induction of the specified children.

1:50:00
And this is what we decided did. This work.

1:50:30
Yeah, are you?

1:50:48
So I'm telling you, you're gonna mail me this distros, I'm gonna help you. But the first thing that you produce, where is that, rather? That is not much interesting.

1:51:04
And then when I on that understand, Thank you, they should be wrong. The study is part of what I'm using. So, that does not understand you okay? I did.

1:51:41
Just keep a.

1:51:46
My friends that I've seen I have to see you, there's no way.

1:52:03
Really always to the end illusion is another one is

1:52:28
That I feel about, definitely.

1:52:48
Supposed to be very and things about the program. Okay. Just to make sure that everyone understands he's filtered cannot work. If there's not enough program outside, I mean there has to be two machines outside one that's since daylight wanted. Actually, the code for this under the subject is part of, I mean, sometimes things are good.

1:53:16
That what we're doing. You're right into currently. You basically have a the text box box in front of her A environment to me and you don't know what those are at this point reasonable consumption. So if you're not, you are writing the code for this but if you, if you don't have an environment, I mean am being never changed, right?

1:53:46
Nobody gives your data and what he uses your day, so but you know, write the code under somebody's some as a program, so they have to give you free to data usually. So, So here, it's supposed to AMP after the HR0, nobody has given me the data when I start.

1:54:09
And I only think the data is given to me, If you build yourself was, here was, well, be 0 and you feel something out. B doesn't change it. Okay? What if you? So, what's your name? Third statity. You have the seven. You have filtered at the six is still seven.

1:54:30
Or is it here? So something that you're making about the environment.

1:54:51
Is back.

1:54:55
It's so much more good because well I want to help.

1:55:11
Yeah. So, that was my favorite thing going about my agents, the opposite here.

1:55:45
People to wondering what to do and what we needed earlier will use the drop and if I can get it before you of

1:56:33
Holding. This is what it is. It's competitive. Therefore, it's aliens here. Yeah.

1:56:53
Go. And,

1:57:00
Into the around. Yeah, because it's

1:57:11
Zero, all that.

1:57:17
Of course, I said right, you can review them. Okay, give me a chance to divide our order. The.

1:57:28
Relationship with technically, possibly.

1:57:37
Say that I divided before the you know here and so here we have a kind of exponent. We have a 20 to need to do just making this is we know we've done the program again. So, if I feel very good,

1:58:11
So some something is filtered passes the filter. So if any divided by x or equals 0. So this is not, it's modulus. Yeah, but it's so this is a multiple of xy. The definition should be drug, it's something out. Oh, so anyway so I can I can basically to do this if it's not filtered out then you transfer to A to B, okay, capital problems on a number one.

1:58:58
What is the value of B? Yeah, since probably would be seven where they could that statement there. It's gonna happen. No, it's been overwriting. Always going to send it to zero, So it means that the environment never gets the filter values or it gets as something. So that's not reasonable.

1:59:28
So we have to make sure that we turn off with the environment. See, like we shouldn't be zeroing. Our the B, interestingly the symbol of the environment that actually, you know, we have, I mean, the environment have seen the value. We need to know that there has to be a feedback.

1:59:46
We need to tell the input. I've seen your input and you have to environment. It tells I've seen it out so it really has to be something so you know you can define something like it and drop.

2:00:05
And then we have any commodity on an equal field. Okay, so let's say that you have, you are going to keep the value that is in a, okay? Then basically these going to these gonna get and he's going to get the zero to tell the environment that we use it and then be gets a if him.

2:00:38
So if you can have the value A and translator to B, but we also check that, you know, A is not 0 and we need to check that V is equal to 0. We have a place to put the value and we have actually real then. Okay, then they have teal down if you don't keep it, then with the we do what any becomes?

2:01:08
They become zero, we have used the value and B, because B, if drop and a different from zero and don't carry these 0 because they know what? We don't modify being. So the environment may be keeping a value 70 B, and I can filter all kind of values to drop.

2:01:40
That's fine, but only get a value that we actually going to put. And we have to make sure that the environment is red. And so what the lesson here is that you have to have a protocol in which you're dealing with environment, not just a program itself. So really what you should do here?

2:02:08
Is environment that it can we don't care that they're too environments are not, it's our generally environment. It has variables A and B and we're putting those for programs together, right? And so we were going to. So now the problem that we have next is to understand by what F does.

2:02:42
So, how would you approach that?

2:02:48
Episodiacity program in its inputs. And during thousands.

2:03:03
KDS all my specify that,

2:03:23
You.

2:03:30
So here's an example here. You've got seven states, age, 13 and God could be. 7:30 what are they suggesting? The relationship and he finds relationship between what comes in and what goes up.

2:03:53
And it depends on what comes in. So the bottom line here is that there is no way for you to specify this using kind of use your basic arsenal of, you know, you know, stable and leads to its own. There's no way to do that and maybe two things you need to do first thing, we need to introduce a very variance.

2:04:31
Second, you need to introduce environment.

2:04:47
It was QA. What do you think is very able to do?

2:05:01
And how do we introduce them?

2:05:06
Sort of the latest QA, hold the input, to behold the outlet. Thank you, history.

2:05:17
So then the, what? This advised us creates a relationship between these two history. So the QA was this and QB is that we can tell is this product or not.

2:05:39
So we leave Indonesia very variables and we need to to basically reason because of the specification of the program in terms of anything. So the first challenge of you in the next three minutes is to figure out how to fewer and can be, are observing variables. So they need to be added.

2:06:13
So how do we define the updating of QA and giving?

2:06:25
Let's go to a updates of hey, environment their environment. So they must be in their environment, a statement of equal text, right? And what what x has to be greater than zero. Hi. And today cannot be. So, if he's equal to 0 and x because I understand number 8, right?

2:07:14
That's updating your baby for you do this. We need to add the history because it's adding a new value to A. So basically in parallel we have to say QA economy through a God animated music, text he became for zero and X greater than zero the same condition. So whenever you you changed a of positive value, you need to update the history and this is done by environment.

2:07:58
Now who's putting values in being the filter, The film. So,

2:08:09
That's where we say B on equal x by 11 right. So that's what we need to parallel can be. So when we take the, when we take the D from 0 to 1 0, we add that into the history or anything that A from 0 to 0, we had that in the history, We don't really need to write the code but you need to understand what the code really means questions.

2:08:45
So the second night of the QA equals QA, let's concatenation. Oh,

2:09:06
So, the other things that would be helpful when I need help, when it comes to reasoning, the one is going to be the ideal prefix.

2:09:22
You can see that eight lines of prefix of a of H2.

2:09:41
So, so you see that H2O is h1. It's a beginning part followed by age, which is kind of inverse of the way.

2:10:03
So, that's an important concept to be able to compare history. And then if we want, we can have legs.

2:10:18
On the

2:10:23
Okay. So now that we have this capabilities, how to describe the correct behavior of the film specify, the name of.

2:10:37
So you you need to have. You need to have oxygen vehicles. It's only way to specify the ankylosing we bypass that in the, in our router because we just put the history already there. But this is the way we know. So what do we? What do we want to filter to the?

2:11:21
You should have some properties.

2:11:28
Normally here in.

2:11:39
In have advice.

2:11:49
So what should those properties?

2:12:11
We could say that something is in cue a MTV, if it's the case it's not it mod. Anything that I've connected is not zero. So we can we can help ourselves by introducing some again, some function.

2:12:41
Do something like builder HR next and that drops out of the sequence, all the things that are divisible with elements of. So, you have prefix lens, we have filter, we understand how these are updated. What does a filter do Not just this weekend?

2:13:20
So perhaps, I told the function isn't adjusted QB equals filter, QA X, if you. So basically you are saying that Q being equals not there QA. All right, but there's a little bit of a delay in there because maybe you didn't consume only, that's too strong.

2:14:06
Probably awakening on.

2:14:14
You shorten it down to a link. Well, I think generally, if you say x is equal to y, and you say that's too strong, we say instead of doing leads to excellent, then we go to my that's weaker, right? So how do we weaken? We convict. He is like this like Laura when it could do that but I mean, but we do have this emotional prefix.

2:14:56
So what do you want? Is this is if this is a QA QB, create might have additional one additional number, as you're gonna have more than we combine filters on it. So again. So basically, we want to one want to to be a prefix of the filter QA. So, to

2:15:34
Okay, but I mean, that's not good. The we had this for my heels so we need to write the

2:15:54
So QA is consistent after certain points 14. So it should be. Well, see, that's an important point about more stuff. So, you see this relationship between the inputs and allowance. You know, the H2 is H1 because as a negative rate, H1 is a prefix of H2.

2:16:32
Yeah, he tried. He's appreciative scoop h1 and can be more engaged to this. Same feeling great. We had more And these would have to be any value safety property. It's a good and that defines now.

2:16:58
We have this then basically, we are maintaining consistent with the results but we could have a filter which basically says, I don't know. Care about you.

2:17:18
Because I want to work today. So what forces a filter to do something? So safety properties were going to property forces of health individuals. I'm not quite usually proud of this property.

2:17:39
Food store at least now, right? So basically what we want to have to deal with is the fact that the, you know, if there are people, if the filter I mean I'm not writing complete formulas down another If the legend of the filter his smaller than.

2:18:07
So, rather than QB, then QB must increase. So we can say something by the alpha and legs of QB is smaller than filter. Keep filter UA. So, it means that we already cross. We've got a more input but we haven't put it out. Actually to

2:18:48
Actually photoshoot to, okay. It's to, to be greater than

2:19:05
So that now we got the a safety property, this talks about the consistency between the historic efforts, the history of outputs, the progress property, which says that if there is still stuff to be reported to be generated, it will be the downside to the two profits. Now we want this property is in here.

2:19:37
So this ideally, you know, these are the conclusions and they have to make some assumptions about. So, these are properties in the text.

2:20:01
So to be able to do this, we need to make some assumptions about the day value. So what would be a summary reason about the environment?

2:20:21
We're back in government for the next week. Just think a life wouldn't be reasonable seems to expect.

2:20:35
So it goes like the way it doesn't decrease or, you know, I think that's the reason.

2:20:45
So if you what they expect, is that if they environment is put in a value stream there That doesn't change. Mmm. Massage. That becomes. So, a non-zero value in the input is stable.

2:21:09
We can't require that environment to put announcing a value that may or anything to filter, right? But if you push one, it has to wait until the dollar only. The filter picks it up and please stop by Martin Garrix. So the stable okay also the history shouldn't change while the variable is located because the history is happening actually nearby.

2:21:40
So, the history of lot of this thing. So once you put a garden there, the history is consistent, and it's staying on that awkward. Welcome more things that the force the environment to become the data. So basically it's a zero, you don't want to environment the factory zero and one environment to put them fully value that so zero should be stable without that's part of Texas safety but it is not zero.

2:22:17
It has been so not available to my mistake. They should be until which is not zero until you can see and that's an obligation in the environment to remove, okay? We'll ride the formulas. At the beginning. Okay.

2:22:56
Part of

2:23:20
With camera.

2:23:26
Yeah, so many other people. So, yeah, so you can apply questions. Okay? Now, if you're done, I just Yeah.

2:23:50
Will location of that.

2:24:10
Yeah, it's a function. It depends on your model system.

2:24:23
If you the name of their high injury can also information smooth proud of which is none others. Okay. So, for argues, we only

2:24:49
So good, for instance. Just a little, I don't know a cheap way of doing it. Is just use zero zero same location, 0 0, 15 center road. Okay, because there's music here. But yeah, but in it doesn't matter what it's about. You just have to have a symbol for locations about.

2:25:15
So, we basically say in Indian, JJ G, or which means

2:25:37
Make this. Again, I told him he of their

2:25:59
Okay.

2:26:10
Or you can turn off the Jesus.