01:24
So what is I'm right here. The party dressing. Everybody was known for presenting.

01:39
Different enough to raise your hand if you're just like presence and body. But not.

01:51
This is a great family and I was like extra credit stuff. It's always alone. That's the answer. Yeah, you've ever

02:08
Can I be not yet? And I got some morning or something problems with government but I do not get from everybody. What's the definition of really? You must do it in your compulsive if you wanted to get the best of course. So I can fill all of them. Technically, since I announced the beginning of semester the rules.

02:45
All right? So, they have ceilings that three.

02:56
I know you want more. Hello? Like if you said five weeks you can get private today. Just so it's really that and so on what to do when we get today into more, you have one more one must become more sophisticated than previous one. I had two.

03:28
And that has a one was actually quite interesting. If you're in Delta Security, kind of issues just looking enough time to bear with me. Like important phasor force in the class statement. Okay, so the first thing we want to do is talk about the last design. So basically, the last assignment you have a problem.

04:03
And you. No, is the sound because I know then we need to write this conformification of the foreground routers and very sophisticated devices. The reason they're sufficing. I mean, what they do is very simple. Packet comes in, and they decide and the one line, they decide I'm not lying.

04:46
That goes out. That's what they do. The problem is that, you know, the routing tables are affecting the, what they're not that does it. Also the system requirement for very high speed. So, 90 second level traverses through the family, and that is even kind of routers.

05:17
Basically it has a great inside, so on the staff comes from this, it keeps on going straight until it finds a output corresponding output. And and then, so if somebody trying to cut across count because there's a blockage there. So this guy needed this, this guy wants to go here, but it can't.

05:48
So you have to but we are not dealing with design but only. So what the outer does basically is going to take in our case. Could take messages that come from a source in the source and continue to understand.

06:12
Now, messages or systems of better, the tail can really body. So the message is divided into packets equals ice packets and we have the header that the first packet tells not just the table which is message. Contents has been said and then there's a fair of a set. Typically the leads to the front, it had one kind of package there.

06:59
So for instance, two to say, let's say one one means head zero. The body in 00 means tablespoon. So there are not important the head on things a source.

07:40
So what in the heck? The message, one of these source and use how to. So if he's coming J here,

08:03
Is still, it comes in and come down.

08:13
Wishes of. So if you have the first one, but from the table, how do you defensive? Because there are two messages other than just each messages ahead in the tail. Mm-hmm. So the first one comes through and then the second comes because they have the same source and destination.

08:52
Yeah. And we couldn't differentiate, but depends. What what you mean? I mean, if if for instance, I send the first message it and then I sent a second question and go lower the screw right? Yeah. He's my first person. I think this message is here and in the second message, how is that for him here?

09:19
And then I said them out again. As long as I, I maintaining journeys as much as possible. So how do you add different them and want or two different and messages? Each one has a hand in the tail. Yeah. So because they have the same. You said, but I mean, they, they cannot overlap.

09:44
So once a tail goes through, the next message, comes right. So because that the next thing I give you 25 through that walls, I give you the first red ball and then I send you the second there's no confusion. You may be confused about what the two mean but I'm sending them in.

10:07
Yeah. Because the message is divided into package. Yeah. Yeah it's yeah. And then that too queens of the packets. Okay. And we cannot remember sending this message over at this package of the internet. It's a router. Okay, so it has input lines off the lines wires and then they come through those wires and it goes to those wires.

10:36
So in the even outer, does a job properly, then there's no problem, no problem of confusion because you're going to get you're not going to mix messages and your task is actually to define what the correct router is. So, for instance, a bad router might take packets and dropped it.

11:00
And the destination doesn't, I mean, unless you have someone so information, it's normally the headers, the headers going on. We don't have it in the far problem. So since I don't have the number of packets, I can't tell. It's a destination that I need to, okay? Also don't every transmission of conversation back in the internet because we're not going over a graph by going through box of circuitry, from one end to another.

11:27
So the properties that you need to to satisfy packing transit, cannot be modified, many more. So he finds in the packet. He can't change the value inside. It second packet folder, he doesn't message because we preserved. So if I have at one time too and I send him in that order and daughter is determining by the input line, right?

11:52
So shouldn't either that any exactly the same one. Yeah. So for those are our. So our file, How do you charge adding that information into the packages? But you need like a specification which courses that are out of desire to guarantee this properties. Okay? So you don't design the route.

12:16
The offer is a black box with something goes into the rifle. Is there? Who don't know. We know if it's outside of the router, let me know which on the input inside or outside, but you don't know what happens. Okay, so messages from the same source going to the same destination.

12:37
Must not be reordered. So, if you send two messages from here around there, they have to arrive in exactly what messages from different sources going to the same destination, but not meant to live. So, if you, if I'd send message from here in the message from there, J, they can arrive in any order but they cannot be mixed of your message, either this.

13:05
And I first leave each message, the decent must eventually be delivered. So it's not possible for the router to suck in a message and just dropping an attraction. And by the way, some routers do that it's overloaded which is I'm and that's started. But those are the properties that, that is router has beside this one.

13:39
So you need to write basically a formal specification of the behavior of their doctor looking should be important without even language.

14:01
Just going to.

14:06
Can also again what's the switching fabric is a code the circuitry that runs around. Yes, and why don't for us but you mentioned some limitations you say I gave you an example. Oh, the very specific kind of router that many different routes. So so they are, we don't have to switch between here, they call.

14:37
They can have buffers, they can do more kind of things. We do not is going to look like inside. Oh, so we have them specified formally how the router should behave. Also the one you mentioned that's just one example. We don't have to We don't have to follow that or okay?

15:01
All the inside of the round. Oh, okay, I'm not designing the router specifying the behavior, so we can just create that string of messages as one. No, you have the message. I mean, every message has to be divided in this way. Something, it comes inside from each packet is messages may not packets.

15:27
And you have the header and the plan, the paradels on the message starts and the tail tells you and issue that we don't get smartphone submissions or messages. So he can't just treat as one. If you didn't just find them. It's not proper. You just take it from here and put it there over destinations when it comes from, which line, it's comes from and it likes to go down.

16:12
Okay, in general, if you are trying to specify it device like this where basically because they react things are coming in world when they're coming and how they're coming. And so on, The only way to actually specify this natural, use of generally variables, you are not going to do that not in this way.

16:39
But normally what to do is is a router and internet, simple device like this introduced auxiliary variable, which is a history of everything that comes in and then your specification is a relationship. Okay? That's gonna, that's gonna get very complicated. So, what I'm suggesting simplif in your life and what you should do is, you should basically build an array,

17:23
Okay, so this is let's say one comma one. And so the this section of the ray corresponds to that other, so we can't really give us but assume that the all your inputs are already preloaded, you know, in the important. So all the messages that you'll ever receive on my mind that already here, all you have to do is feed them to the roof.

18:00
And similarly, you can take this output. This is basically array where it can continue to have messages. Now, you can't override messages. So if there is already something here you come over right then but everything can move up. And and this way you can you have in some sense you have the history of the future of the history of the past or any built-in in a very structured way, divisionally to assume that all the messages are here and you assume that the output lights that and in the area this area, obviously there's a better because they can't get a message area.

18:52
And this area even though it matters is really inside a switch. So you don't know what's going on there, so you don't worry about that area. So, you basically test me this arrays who help you. So each cell source of packet in the pack is set into the router.

19:16
And then there are other features out into the output lines and output lights. Consume the packets of the sense that they move up to make room for the okay. So that's a major signification. Gonna make your if we the thing that's going like this is all messages. Yeah. You put all the messages from like one.

19:40
I don't know. Oh, so yeah, the news they were around in the future and we've added those and so yeah you have in we have one to end and once again I can just create one array but we use it properly. This section here is useful for inputs. That's just for output and this section is never used because it's inside our but that makes your life easier.

20:17
Okay. So that's one. One one hint that really can consider by saying someone so all they with messages, they will ever arrive on this there and then the problem

20:38
Okay, another thing that NCP find your life. If you build something definition like you're gonna happen for the source of the message. Well, I don't know one invitation that I use, but

21:01
So if the target was alpha just as an example packet was alpha, I could define alpha towel to be the time. Is it a header to pack it or anything? I couldn't find. You to the disadvantage being carried, They had a resume that they had is empty. His guy said values, and I want to the source of there's our singing source of DS.

21:43
So the point is that I'm trying to convey that proper notation can simply find your to make, okay? So I'll give you two inch. One is user raise to represent the task of the future. Submissions assume that the submissions are correctly laid out on the race. So, the headers in front of the packets, okay, Introduce proper.

22:14
Some definitions that allow you to talk about so much destination and other packet. No. You can also do things that, you know, we talked about a daily variance there was a not really in the system but to be using for purposes of reasoning for improving things. So one thing you can do for instance, card additional information, to all this packets.

22:48
That is not really sim handled by the router but it is useful in a specification. So for instance, if you want to be able to talk about the third packet, you can't tell the difference between the 30 packet and the forcepad but you can introduce the packet. Number is an oxidative variable in xenia, fielded is virtual is not real, okay?

23:17
But is used only a specification. Yes, could not add in the message, aside to any messages. So for each packet because they are the same time, we can know the how many targets for the inside of the? No. You don't know how many because the message could be different labs.

23:36
I can I can send that five gig message with one file or I can send you three k. So the number of packets in between can be very to that one face, but for racism, you could have a, you could have a, you could assign to each packet. A number where the header is one, and the tails, whatever.

24:03
Okay. And then use that in your specification, you can do one. Even go further than that. You can assign a message identifier to each bracket, and then rely on that in the specification. So the very first thing you need to do is essentially what make the assumption that you're going to organize, okay?

24:30
You put it off, maybe something without produce an empty and the input of raised contained, all the future methods. Like the sample that all the message are properly. Structured head packets tail and then decide what kind of electrician information you want to attach to each packet and build functions to be able to talk about that information.

24:55
So if not attach a message, I unique message, ID to the packet, to the message and your thoughts area. If you pack it and you can say this packet is, this package are in the same message or not. You can have that language expression. So, you have to decide what observing properties you're going to this component.

25:20
They are not real about. It cannot use them. You can use it in this and then you find functions that allow you to talk about this properties. So you could, for instance, assume that the, you know, the lens of their message, had that very out of virtual actually good to each pack at the legislative if you need them kind of questions.

25:55
And but here also, information 100,000 were coming from, and want to go some source of destination, which are two numbers are coming from line, one. And I'm going to line five. Also, let's not like real life, so router where we have to map the IP address to IP address.

26:27
Why we sound so IP address the actresses destination. Yes. And the, in the router texture IP address transported into output line and says out for IP address. Once we several pop-up, I go online five. So we don't care about that. Oh, oh my one goes to nine. Five four.

26:52
Oh, three, you know the question?

27:00
You need. I mean, you need to make it very clean and all this properties. Are once you are five, you need to be able to formally specify things and then and they make other properties that you'll find helpful to specify, which I'm not captured by R1.5. Says, if you had inputs, you have data on Android line That data should arrive at the router.

27:33
At some point, if you don't have that property, then basically, you are telling me your specification, says, you can cut the line and I don't care or a specification says the router can refuse messages from online streaming. That's not good. I know that was justific so or you can, you know, you this packet is here and on the output and because that pocket is there on the output, you can't send anything ever.

28:09
So you plug the drive system, I don't think that's an alternative one to that. So that. So the router basically that any three components, there's a router is a component that input lines and often lights as components. The input and output lights are in the environment. And we're going to talk today about composition.

28:30
So that particular environment and the environment and the router network together. So the router is going to work properly. Others have to send the assumptions of the environment. So like for instance, if you put an message on the output power, you explain the environment to consuming if the environment is besides what to consume it.

28:52
There's nothing that after can do. So the router is correct. Only in an environment that consumes the messages. It's also only corrected, an environment, that supplies messages. Definitely drop. Okay, so how do I model dropping a message? Basically, I take it out of this array. I take the whole message and that I see all of those.

29:23
All those then you can assume that you know, I mean if you want to zero, this is nothing or you can use a knob or zero indicator that cell is empty. Souls was a found requirements for the message process. Are they the also requirements for the older messages or just, for example, the specification, for other routers to do for them.

29:51
So for all the messages? Yeah. Okay, So each message at the same must, eventually be delivered. You can drop the message the trash and they have to be coming out in the same order. If that coming from the same distance fun. So I treated. And so, make sure that in your, when you present yours solution, very carefully on having to ride, difficult routers, any variables, oxidative fields, that that you may need for specific.

30:32
Make sure you have one of the all the proper functions alphanues and packet for anyone in this. Maybe you want to say that alpha is in a particular location. That might be a consequence importantly, then introduce rotation for that. And right in English. This is what I'm saying. Trying to say in this a format that says

31:06
Why should my solution is basically half a page of definitions in a full page of photos, so it's not an easy, it's not thing. And they talked about the warmth or I told you I had to postdoc the work from the one more router for six application of six months, but it did a problem form of treatment that we have kind of

31:42
You will say your solution is half page. Definition. Oh, with English. Oh, with English.

32:07
And also we may have to make some assumptions about properties of the input lines that you know, which means messages were not given broken messages. We don't get too tales, you know, two heads. Okay. Now, let's talk about the homework that you have you today. So, the way to think about it is that we have a board meeting in the board has lost

32:51
And slot. We put a check.

33:00
And that's one of the create our pipeline. No, it could be nice. If so I allowed you to make process from a zero different from the other processors, okay? Just to make your life easy. But in reality, I should be able to pick up across so zero in moving the location fly and the location, finally is zero in the six issues should feel more which means that a couple of things.

33:33
So here's the last, the capital of, if you are in this position, you need to know the trans.

33:45
And as always, you can't change your behavior, You can't be able to depend here or so to do that we can add an extra pain and that being, let's say is high on this board of this circuit. And this movement, well this part of the board and is no on the rest of.

34:09
So, when you put this ship in, it reaches pain and he knows that he's number one. That is first. Now those things that we need the last one to know. That is the last one. So one way to do this is again, have a different theme here, which basically it tries to read from the neighbor.

34:35
And since the voltage is zero, says, there's no name of it, so we can use that idea that when a cheap shots down the voltage, there becomes zero. So, the next key point, it tries to voltage. It says zero. So is nobody there. So this is a way you find out that you have the last one in the, in the you cannot you cannot use n anywhere.

35:10
In the design, you can write the code that depends on that, because that means that for every shift that I have here, I have to write a big deep switches. It's actually by him. Push the switches down and says you are 0 0 1, you are 0 1 0.

35:30
You are 0 1 1. So, I have to move the switches and then when I moved it, the chips are out. I need to reset the difference, so we cannot remove. That's why it has to be completely uniform. So but can we use 0 to tell a chip is the first one?

35:51
Well, if they all have the only have access to the board and this is this is only one, it has a voltage. Everybody else is zero. The wire just that week's cut, then. Yes, you can do that, but they all have to let the same same, you know, same design.

36:15
Oh, so they all have to have the pain that they read and says hey my number one or not. So, what am I seeing? Is that different from the switch you mentioned for to in order for each trip to to have access to the number. And Well, it's just different because I do not have an app but you have zero or organically.

36:53
This is a high voltage. So you see that I've wanted and you're not the child one. Oh, the first that number everybody, else of the internet, says there's no voltage there. So they know they are not numbering or and what kind of unity statement does this create a bullion array?

37:16
Oh, and all. And that will make to this kind of harbor, trying to write the code that not. I mean the to write the code for, you know, for this kind of design. Oh, and I see that there's a component can take outside and end up. Oh she that's why you know the pattern of the code was you know, I from one to end.

37:46
What I is is a process of number and then we have the code that goes into the, but it's the same code goes in old process. Oh my unique. You have been in this entire as always to variables which. So so starting with that, we have that approach basically the chip now is modeled we have the beer register here and that so we have here, we have the air and I needed to register to be able to tell if it's on or off.

38:28
So then I have the only difference on it. So I have cornbread to here and then I also have to have access to this information here whether I'm first or not and I don't know what is for that changed it. So, this is

38:57
Then.

39:07
I need to be able to this is a last process.

39:15
Is a nice process that it needs to be able to tell that it's lost by actually reading trying to read paint here. And this pin here is since there is nobody there, that's almost down to zero. So this is always kind of this. This one is false so it feels if it is true and the next one is false.

39:40
He knows it's the last one and on initialize this 10 plus 1. It's always initialized the force. So now the ends process or knows it's the last processor and the first processor knows that is the first processor because

40:02
Now, this processor is that about neighbors, this processor can raise the and this processor can be paid. So that this is the arrows starts on the register that's being read and hands on the process of the reason how the processor uses a value to differentiation. You don't have to tell it that it has to put.

40:31
It just reads. It also needs to be the status of the previous one is going on. So that was a basic, the basic.

40:51
So I'm going to have to have an array for half and I have already put in on 348 and I'm gonna have to have because I want to have the same code on every processor. I'm gonna have the exact same code. I'm not gonna differentiate a zero peace from that.

41:11
I mean, essentially hotel that you are first or not.

41:27
Okay, so now the, the way the processing goes is that I have

41:37
We all know that because rotate the last in the class of processor, we brought this here and got no You made a very important observation which was that in a synchronous machine. Think we care about recommends because you know this A it's read by the prednisone and the predecessor and it's updated by this process.

42:13
But in unity the execution of statements is very multifaced. You read everything compute and then you write everything in the circuit board that we drive that will have to be actually accounted for. So they would have to be two phases of execution where one is given a signal everybody reads, then they all right, and then go back with so they don't have to be some control, we don't need to do that because we get it for free from the way.

42:48
The and unity executes executives statements. And but we do have to understand that that's going to have to happen the phases to avoid being the right confidence And that was a very good opport and yeah, okay, so we're going this way and what's going to happen, right? Is when I get it.

43:11
When I hit a zero here, that I locked that zero in that position. So when zero is not, in the position, this seven is made by the processor. Like in the air. So that's why I see I don't want to I don't want to change the minds of those from D today.

43:33
No, you know, always go to the process or so, that's a value, it then can decide to write and whatever it wants in this world. Okay. So you initially write here, but other than then, we're going to get the second zero. Then we know that we're going to try.

43:51
However, there is a subtle thing here that you may not have noticed. Let's assume that this is a mission configuration. Okay, we haven't executed the single step. This initialization have happened to have two zeros in the last process of my question for you. Will that process shut down? It has already snowed all the most of us from.

44:22
Yes, so even though it has to zeros, we're going to circulate one more time. We're going to hang on to this zero. Okay, but this zero is going to below because when the way you shut down the processor is by looking at, I read a zero from there and I have a zero here, that's a condition for shutting down.

44:53
So if that's not a zero there, we're not shutting down in this, in this step. And the reason is that this processor doesn't not have access to all the information has access to the steps of your own, so kind of make that cannot make decisions that. Okay, any questions?

45:22
So my mental block issue was, but if you have an automotive zeros then one zero is going to be stuck here for yes. But when we're going to the situation, the thing, that's the proof of this. Yeah, it says we're counting. You told us to do counting across the service.

45:46
Yeah, so it won't show you five zeros, you divide by two, you'll have a you have to have two plus so that you have shut down. Yes. But then the zero won't always be in the last. He just lost in, how can it not tell you have. So you have a hundred processes.

46:04
Yeah. And then but your four zeros right before you enter the last thing. You have your zero down, here it goes. These processors shut down. This only move four percent and has to go all the way over now. And then, we end up in the in the last processor and register the right.

46:29
You're gonna get stuck there too, says that it should. The six point is who don't have a fixed point. It's running forever where circulating data forever. So it kind of then new the yeah first yeah almost is that the number of processors that are shut down. It will write on the specification event.

46:52
But the number of processor that you is equal to half the number of years using indigent, I need doesn't require them. I mean, because of our code is even going to be captured in the top external velocity doesn't have to be. It's a water deliver. So, any any questions about the design in the motivation?

47:22
I came up with a different solution of the person. Heated. It was like, you always rotate, but then you have a like, an on/off space where you just rotate it back. If it's just, you just get more confident to disturb it. You want to the circus clean? And I know it doesn't.

47:43
I also needed one of the problems I had some of the more was a fact that I mean, how would take me half an hour to figure out in this correct. It shouldn't do it. I should be able to tell since I know the problem I should be able to tell him to minutes and because of the definite and the naming that was used the formaza produced.

48:07
So, for instance, in some, some homework, you know, people checked in the in my processor to the left. It's one. I can do something. And the reason for that is because there is a property that if this says upon I'm on also but you have improvement that problem and you do not make the explicit in the in the circuitry.

48:33
I mean do you want somebody to prove the circuitry? It has a certain property so you can cut down one test. No, you want to make a circuitry as simple as possible to be reliable and predictable.

48:48
So, let's, let's look at possible cleaning because so woman,

49:07
So declare there A and B.

49:19
Natur. I even like the code on the board because I think I can talk, so I know it's idi in the box.

49:55
Brain of that was

50:04
Usually,

50:11
We have.

50:20
True, we have.

50:51
So basically one is true, I want to stroke. And for I is equal to zero then I provide square. So only the first one true or doesn't become and always, we have the

51:16
One.

51:20
This corresponds to the pictures of the wedding.

51:32
Part of box. I on zero time. So this basically says, everything that follows is for processor pi. So two things pressurized has local variables that can update because our I can read separate variables from the neighbors. According to the diagram design, have to make sure that that is compatible, Obviously have redirected access to your own variables, but you have to make sure that you have great access to the names.

52:08
The thing is that you could change the design so you are trading right to the name, but generally that's a very bad idea to allow someone to write and have somebody else again. And somebody else is, it's okay to let it read but not to write. I mean safer to totally rewrite.

52:31
The number of but you have to make sure that whatever you need, it's an accordance with the rules. Some of you have actually, you had a diagram of the design in one way, but then you would actually write in the code. You'd write to your name. Could come with it.

52:54
Good morning. I'd like to your own bags. You can read. So, this is called for everybody. So,

53:13
Okay.

53:17
Let me separate. You know, was nice and cool. Any. So we have AI cover. What are Nicole? They are. Yes, I plus 1 and I

53:41
Who has his behavior you get from your neighbor and you push which process high zero. So you can invest if you. Are you ever wanted to? So you are you are you've got a single that you are the first and going on. You see I can read this. It's first and it's all it just is behavior in this one below from the right and then pushes up.

54:22
I mean, you can see we need it part of our, okay, the eye. So,

54:43
Okay. 5 plus 1, comma, B 5 minus 1. So, I've reading from the for the, right? And we have into the air register and everything from the left into the B. When can we do that? Well, it can't be the first and that's all here. We have to order to be on and you can't be the last.

55:18
How do we know the term of the last? Because the next one, it's on. So and or by very easy to read, I'm not the first I'm active and I'm not the last because the next one is actually, I don't even read from the next one. I read the V from the previous on the left and in the, A, the diagram had exactly those arrows.

55:47
That's exactly. What? Now, the last part is more complicated because the last component is as different behaviors at different times, If it has no capture zero, you basically does, you know, read from here whose disorder. And if it has a capture serial this one there, but movies and server.

56:10
If it is this is a zero and this is zero. Then this becomes the zero, and it also starts off in the same step, So you have a couple of different behaviors So you have to analyze them all. So,

56:39
Of high. Company called nearby heart.

56:55
Hey, I know the first and he wrote his heart writing in the same order. So when you go down that kid in an easy and I'm on and the next one, it's all. So I'm the last, I'm the last

57:23
And again, I is not here and that's a behavior basically AI. It gets me and beyond because they might Next.

57:52
We have. Okay. Hi Colony. The video. I just want.

58:02
Okay, another first. I'm on and last.

58:18
So see, this is not getting the value from there, behind the scrape into here. In an effect, the time I was trying to go to and then the last velociation

58:38
Hi. Hey, I'm not the first and I in the next one. So 10 BI is equal to 0 and B, by this 1 physical

59:09
So, To anybody said, they

59:58
Great questions.

1:00:07
So the names help a lot and they help.

1:00:18
So in the career session the other way? Begin from one of zero, don't say? Yeah. Oh, That's 0 to any minus.

1:00:41
You know, questions.

1:00:49
How great one also we just shut off the master. Once when we read the contents to zeros Well it's going to contain for 0 because yeah it is 0 here. I'll return this one to false messaging as 0 here, the same cell because you I don't that for that.

1:01:11
Step is here. See if B1 is ordered, BI is already 0.

1:01:21
So the eyes are any zero. And this one is a zero and take this zero and the master tube. Now will go over the code. They just see this one is not possible customer at 0. Yeah. So take some there and put it straight here, and the number and also notice that they are all distinct

1:01:53
No, the master tube. So what you're saying, it's the longitudinal cold. There are not this thing with each other, right? So that's why I did not have this.

1:02:10
Because that was taking me getting to zeroes here. Who knows? How it's confusing about and the other questions problem, that the greener the separate to put here, the island of one company, you know,

1:02:42
To have questions. All right, so let's go to the experience. If you have a lot of problems and he was a specific and so, so let's go slowly. Okay, so we know we have and plus 1 processors. All right, let's see me the number of zeros in a system and

1:03:21
I have to be careful that. This. These should be the number of zeros to the initial in addition. So if you go here, what you're going to notice is that I don't have a way to refer to the new some states. So I probably should be actually adding a equal, A, in B, equal B.

1:03:51
And then the number of zeros.

1:03:57
People. So that's a problem.

1:04:06
Then let's say we have k.

1:04:13
And it takes. So so we know now how many processes of emissions are done. We can also use. I some of you did this number of idle process. So, initially conditions, see then and you can, I mean, you can define the idle as being not. All right, so let's assume this definition.

1:04:54
So now that's looking specification. So we always have I don't know why. Some of you really just refuse to. This can stay the most. So anyway, you need Please do post student. That's understand the definition. We cannot use fixed point because it doesn't

1:05:31
So here's a, we need to be finding new temples.

1:05:42
Okay. Additionally, five different young that. Nobody processors and in the end high,

1:06:04
Now, what's wrong with what I did?

1:06:14
He was already defined all it's about constants, so it's okay. I could have said here, you know, the sound of zeros, initially to z and casing, but I don't need to because our definition. So when you find eyes a number of vitals, we just sum up every single some of you have done that over and then it's a comfor you.

1:06:39
So if we had seven processes of seven zeros, the number widens. So we First of all, the focus on turning things out of currency off, can some of you specifications believe in buzzer talking about what, what was to go. But that's a purpose at least initially, before you discover The purpose of of the program is to choice and go off.

1:07:09
So you'd expect that to be in. Yes, but my way to do that is through a function definition, which I count the number of zeros in the process that is on. So for example, you know, yes, so that increases the counts. The number of processes that is of. Yeah, there's another way to count another project.

1:07:46
I mean, this is really what this exactly what this does. Oh yeah, common one for every processor. That is of this just submission. Plus. Yes, is. But what is wrong with this specification? I mean, it's a most compact. Nobody has come up with this com. But what's missing number of zeros, but numbers even stay the same right in the processes.

1:08:26
That is on, okay? So there are two things that are missing here. First of all, if this not the processors, this is idle. Exactly. So the processors and to turn off should be. At the end of the play, can be in the middle. That's not telling us that also if that I don't actually want to date to be able to zero, that doesn't tell.

1:08:56
Us is. So that information is missing. So how do I handle that? Well, that two ways to handle it. My post is too weak. Therefore, I had additional conditions. So I said, and this property and this problem and that's a way that much more element if you

1:09:25
Added with a specification. So what is this? You have device. I can have any who says a number of zero doesn't change the

1:09:48
So number of zero initiatives, you see? So, and RZ.

1:09:59
And basic says the number of 0 doesn't change. Another thing that I can say that I don't high implies, they are high. Why here? What I do.

1:10:28
People and highlight, So he threw an idol. It's all zero. So then takes care of this condition here. Now I can also say that if you're an idol everybody was above you excited. So, I guess they, I don't I implies

1:11:03
Guardian, why. And,

1:11:23
Eyes, I don't know the name of the design in my

1:11:32
Guys.

1:11:38
This one, but I have to make sure this is Great.

1:11:52
Your neighbor is a leftist So I can write this in guidance. It's very simple, very clean. And now, I can get the complete specification without making it post more complicated. Not only that improves the stability of prose and into proven this. Because these are not invaluable which I did, so I don't need to worry about it.

1:12:18
It's much easier to deal with. Okay. Now, what is the matter?

1:12:35
Well we we have another of we have a number of idler processors and we have a number of many processors to be hiding. So use the finest, okay? This is how many people idle minus. I that's how much more water that's not to do. So if I need to shut down four processor and I shut down too.

1:13:06
I still have to shut down. Tomorrow is, well, founded because when I shot on all the process of anytime, the bottom is being. So this is always, it's always great to remember able to zero. So, it's over form.

1:13:27
Okay.

1:13:31
So a couple of things I need to do One is to prove that you think of zero implies post. If musical to zero, the only way for this to be zero, it is I is equal to k. So, post is implied. That's what's nice about this method. And this specific So 0 is the same as I equal to the k.

1:14:03
And I got k suppose very simple to No, they've been a problem. Some of you use that shoes and you have to be very careful. I mean, this is not. I mean, some of you basically know that if meaning of little computers, you know, it's things to is to

1:14:45
And some of you happy that this was an issue because everybody company ensures because there are many steps. So, to accomplish this, they have to do the saints.

1:15:03
Is our pipeline in the zero. Here, the zero there and this is the end of the bypass. You need to bring this zero here. How many steps it does? Well it depends on the distance to here. Then you have to here all these things. Again, the best of the newest.

1:15:27
So actually we need to bring the second zero here in there. So what you have to do is basically have one metric, which is the nearest zero to shows the reduction for the arrived in the B register. Because on every step we shipped, that's an issue. That shift is an insurance.

1:15:58
But get from here to here, is transitive, they put this place to improve that basically created distance from from this to be registered. And then you show that the distance it is on every single. So there's one. One proof. Second proof that you say there must be another zero.

1:16:23
Okay, so then you computer distance from that as a zero to this position and short for every step decreases. And that's ensures but just transitivity to reduction, to get you. So now when you have a zero here the zero there, then you turn off the process of and that's when it shows.

1:16:50
So you get two tragic. So you just try to take a capture the first zero. I capture the second zero, but in the previous cell and then in one step, I turned off in collectors. I mean that's a way you need to explain one metric for the first zero.

1:17:17
The distance from what it is the another method for second zero don't care about this but the distance from our is to the previous processor. The then and ensures that Combined with that, it gives us finding the so to prove this leads to, we need to prove two inductions each one.

1:17:53
So, any source and an inch was

1:18:01
So so basically would be like no, you know? The let's say LS, the last is not going to be out leads to one. Zero needs to one zero in.

1:18:34
Leads to

1:18:39
Processor. No.

1:18:47
This step is an insurers. These are all linked to improvements around supervising.

1:19:02
Pres questions for the second understanders. Third not the colon here so you can see it the prepaid for the second understood. They are just about the master equals. The Yeah. Okay. Mission.

1:19:40
Over here. Here that's different. And all do you difference there and it is not last. This is not here in the next one. It's a lot of. Yeah. Okay. So I see basically this belt is the case is zero.

1:20:14
This delta is 0. These developers in the middle.

1:20:24
And this elders divas.

1:20:31
For the coldness of structure, the lineup. Exactly. We've got analyzing between environment people really focus on one and reason about.

1:20:49
And so the third invariant, What does it mean good. The one to my right? Is that the third third one actually here and oh and the fourth one, Of course on basically the max going to the left is that I is smaller than 0. It's great. Oh because if it's 0, there is no 0 minus never.

1:21:28
We don't have a minus minus 1 plus, so 1. So actually this works. Even for the case where you are allowed to that, we have four, at least four non-zeroes This works. Even if we have.

1:21:50
Except for a case, where

1:22:02
I think it works even for the place where you are, the only one.

1:22:11
Because you're gonna take one. No, because you can't take from the right.

1:22:20
Is this is still assuming. It's assuming that I the other one is cheap. And oh, can you repeat how you just say?

1:22:41
Only truth process not left. Oh, so if the first and the last are collapse, I don't think this code is going to work. Oh, because the last, it's supposed to move that there this way, and the first is possible that they got that way. And there's also problem with a zero being possible.

1:23:04
Zero there. Nice. So it works as long as one of the last, the first am know that? Listening processors. So exactly the same and can help to invariant. Can you? Well, and let's take an invalid. Like I know advice these two are zero. Well, I assume that they've got it is true.

1:23:33
Oh, what do we make this one? Idle based with on this code, you notice that the VMA and becomes 0, all I'm not breaking their head. So we assume the no pre-commission you assume that they've got, it is true. Oh, and of the code of my brain. Oh, okay.

1:24:05
So, you know, we've got, you know, I don't see he's not listening, you can be active and have to zeros and that is another thing that some of you made the mistake, you've got two zeros in the middle of the pipe, you shut down the processor. That's breaks the whole system.

1:24:24
So, the only shot it down in there. So, basically, when you turn something somebody I don't the register are or zero because that's, that's really the, the conditional, which you are actually trying to get high and then the other is decided, you know, you're turning idle from trying to left.

1:24:52
So you turn somebody idle then labor to the right was already, right? And you can never turn somebody to the left. I,

1:25:08
All right, I know that's all these videos but they think it's anyone.

1:25:30
Okay, thank you.

1:25:34
And then, shaking against a different

1:25:47
That anybody can pick a picture room and

1:25:55
False of it's important. Yeah.

1:26:55
You guys ready for the test tomorrow? Well, it's been a week and a half since our last test about the

1:27:05
And I was like, and it was worth it. She don't know lecture after that class has been one of my bigger regrets in terms of taking it so far. Yes, that is a fact are also learned recently. That was like, Janet Albertsons so much if you made one. Yeah, I made one for my last year, we really useless if you don't have processing power.

1:27:43
So I've been actually doing these work on my own because ours is telling us, I've been ready to rules myself because it's just quicker than waiting for it to try. I love your computer, two days, one time, then get the answer. I sat down for an afternoon and got it.

1:27:56
Oh, we're using and selling our atomic time to model fire. So we can have a little robots run through it. And oh my god, they're fucking stupid. Like yeah, they all run into the fire like, I'm like, so this could be two and a half days to write and they just like like so the opposite direction, right?

1:28:22
But negative signs everywhere and it's still we're supposed to do is or it doesn't take the if you have a mixture of whatever pencils separate someone to all dead and whole life and I was able to write this by hand. It now, it's a huge role, it's 200 something.

1:28:38
That's what I wrote about handouts or whatever. When I hear, it's a computer if you've never gotten close well, like 200 bits is to the whatever. Yeah, but I gave it a kind of help, like, I started to find stuff for it. Like I finally had chases for it and I got to 128 bits and I was like, it should be able to reason to find one and it found a rule that passed the test cases, but didn't pass any actual other tests.

1:29:04
So it just means like, screwing radios myself. You know, when I saw how much reading you're supposed to have done for that, I was just like my gonna prepare much for that example. No, but I just don't have the time for it. I really don't like we have we have like readings.

1:29:22
We have IBM, we have projects, because so far, it's over 500,000 and happily call it, okay? For recommended to read. You can never find her in that room. Yeah, really do think that class would have been better structured if it wasn't that there wasn't additional content. So, I think there's a lot of added content through code that wasn't their last improved prior accessories.

1:29:56
Yeah, well I pandemic just had to happen forward.

1:30:08
So what we're going to talk about is called product structure.

1:30:27
Now, before the just come back and for the homework, what, what I really want you to really get out of the moment with one is that when you're writing that code, you really have to deeply. Think of what architecture because then make. So that this is one.

1:30:57
Something that unique second notation.

1:31:08
Feel can use somebody read your stuff because invisible the right ones instead of like if you're writing a messages that is in the book but I

1:31:28
I think we just How diff to follow. So by adding the next making some additional more explicit as in making invisible, he helped him structure.

1:31:51
Can also become the formative. Health. Isn't every everybody plug. And okay, so what we learned about today's progress factory. So, what?

1:32:10
But this refers to basically composition and when you like code we should be highly modified, right? So we're going to have different objects for both other objects and try to making hierarchical plus something. Buses on You wanted to be watching In reality I intended. But this is 22 and I were, I see code and companies.

1:32:47
There's no different from our guys. So if you saw that 178 2000 year back to. So I mean just is it one? Only think of one, one, big piece of curve. And then they wonder why, you know, they, they problems with cyber more kind of terrorists. They also wonder why, you know somebody, you know, the doing sound like, but, you know, the government contract was a manufacturer to provide the costs of school to the satellite the hardware and software, and nobody can touch because it's all custom stuff.

1:33:32
Sometimes the government doesn't even get access to source code, there's no idea what's that running. And this is just loading the mortgage. If there are divided by most of the time that every go to an image and it's all one one component, it's corrupted anyway. Single and the greatest thing with that software and they didn't supply chain kind of attacks where somebody in some lyrics library, makes somebodyification then basically creates a vulnerability then that they take advantage of them.

1:34:18
And so, some modularities very important. Now, everything we wrote so far now that because it's more formal. Some not every processor for it and I mean, we did not really write the code in terms of towards you like to do. And then for them together, now unity to the abstract station design for different purposes.

1:35:00
Would like to basically stand how you come create modules that work together in a system, One importantly like to basically two properties of the individual models that we didn't for some conclusions, from the result. Well, for me, the most particular important because I was working on mobile computing. So I have one on it, piece of code was useless because one machine was in New York and another one was in Los Angeles and I couldn't even talk to each other for most of the time until they met in some lures.

1:35:47
So, you know, I didn't need to

1:35:53
Having create more systems compose them than they became important to me. And then, you know, I put out that mobility, basically composed of couple things in the painting. But so, one of the things that

1:36:17
Then if we have modules in then and we talk about property or modules, then we have to build basically, what notation to be able to say. So the, you know, the multinational use

1:36:36
Businesses property q holds the mark on program. Collegiate for if you can say, FB fixed point of G. So this is trivial thing. But now we have a notation to be able to to talk about prophets of individual performance which have been defined as we designed something. Now the question is that, how do we put components together and that even in hearing in that two message to ways for comp as in one is more delicate that doesn't.

1:37:18
But that was to the most, common one is convenient.

1:37:28
And the notations basically have box, basically, says, I have the code for graph. I got before G and I put them together. Now how do we put them here about? They have to be compatible with each other. You've got really they can't put the programs together where x is declared in one program as being an integer and other ones because the flow or an array.

1:38:02
So we assume that when you do come common composition, it's about There are the heaves very close to the same name. They have to be compatible between these similar decorations. Now, how do you now reason about the true product between his about the simplest way to think about it?

1:38:40
Is you think that let's do anything of the assignments? The same as they went to a program or just a bag, right? It's a set and this program has a bag and this program is a bad and retaining people from the table and they mix it. So really the composite program could be represented as basically section by section, putting everything.

1:39:08
Just so, take things position section. We think that section, we take the sound section and it has make sort of code together in. So the surroundings of what means to to make is cognition, create a new program, which is a result of this syntactic, you know, subtracting modifications, literally take a text and move it and you create a new problem and the new program is at the properties.

1:39:50
And, of course, I can now see the program in, just a regular program against me before I can prove anything. I want business in the methods. However, I really like to not. So if I prove something on F and I do something about D in to be able to draw conclusion about the composition design, having to put was to the pros.

1:40:22
So the people were questioning that which properties survived the unit and the general principle. Many of the safety properties in this arrive. Many of the progress properties. They're not disapp, which means that you're gonna have to prove the problem properties. That have to work harder before the So do something called the Union Syrian.

1:41:00
It tells us any issue between the properties of the performance and the properties us. Yeah, trouble property one.

1:41:21
Condensed cube.

1:41:26
Box G the same as that's here in half.

1:41:50
So, if I'm able to prove the less property in most programs, it could survive in the union.

1:42:05
Stay insurers.

1:42:10
So,

1:42:18
Shoes team. Oh, that's MG corn.

1:42:35
Ensures G.

1:42:49
So this is what they ensure we're doing, basically the God I've seen that, you're going to make a progress in one step. So I pointed So that statement could belong to P and F or to belong to G. So that is exactly what it says. Investigans enough, everything's gonna be okay as long as there's no breaking down this because in a sewage department or less and find the statement, that is a transition.

1:43:23
So if you find any mouth, it's fine, but you make sure that you have to make sure that those are the analysts in the same thing. Here you can find in G.

1:43:38
So, that's probably

1:44:09
So at this point, something of the combined program to see the combination of the this is America. It's a transfer. So by my definition,

1:44:29
Because if the combined program is a fixed point,

1:44:41
And they have this point of mind.

1:44:51
So property one and two is progress. One is safety is includes known. No least or no insurance. Probably two is progress. Oh, practicing one. Step is any, so that survives? The unions all awesome, the whole system intense. There are less part then if one program can do the job in the whole thing individual.

1:45:27
Oh, because remember, there's two parts. One is on this. Unless says, every statement, what is it keeping pee or taking into queue? Oh, that's true of each of the programs is through the combination because it just more stainless. Oh, the insurance says, there is a statement which going to take you to kill.

1:45:46
I don't care from which on the two. Oh, but it must decision. One or the other. I mean, could it just be both, but doesn't matter. As long as I prove, that existing one, that's all I need. So prove this properties, probably one.

1:46:15
The run to two property one. We started this. And then we look at the definition and this is for all this

1:46:32
The composite some cheap.

1:46:52
So we just definition, we haven't done any investments. We in our cue is every statement because of the pain. Well, in that case, we can separate this. You say this is S these over the union of these two. So we just separated in all this statements and all those things.

1:47:58
So, we suggested the technicians around us.

1:48:17
So, just by using the definitions we can

1:48:30
I'm rac. So, what quite can you put? And the, if I had something in building, one tending building, too, and I can separate, and I analyze first building one, and then analyze it soon. So I get the same result all because this he's understands in the combine. Oh, and some of them are having someone's.

1:49:04
So, it has to be true for this. And that's for all for those things. Oh, what? So this roast them in the combine. This is true. Oh, also some group. Oh so I just choose this to some groups, have to change. Oh and that is me that falls. Oh,

1:49:44
Well, 242.

1:50:12
Again, we go to the definition.

1:50:19
So, we have to have was a few And we have to find a stinger because it takes care of transition. And the reason this such that, as

1:51:09
And that's session for users and this companies understand and there's a state, there's statement that was going to make functions here. It's statement from my current day that we are now.

1:51:31
Beyond.

1:51:44
This cameras as an F, something that and

1:51:57
Form understand this G. Okay.

1:52:14
No.

1:52:29
This be honest Q already know. That means piano is good enough and be honest in. So, we can now basically have these path and

1:53:24
These.

1:53:43
So, she had distributed of course, is all or

1:54:02
She?

1:54:15
But with this means,

1:54:23
This is F, right? It's unless and there is a slender so that the stored and ensures. So basically, we get to big assures that stand

1:54:50
You. So, this is kind of strange and this and that ensures little more. The insurance can on this, and that's

1:55:29
Okay, there are a number of calories stuff who have some concrete.

1:55:49
From one to make this property. Then remember, so one.

1:56:02
Maybe. Three. Maybe there's still no.

1:56:19
Stable music doesn't change. So it doesn't change in the composite doesn't change in the individual is because you have a change in it, none of the statements can. So this is statement of F of 73.

1:56:52
Stable G.

1:57:05
So the statement of GO change P the statements of death and use of the alone.

1:57:19
So that we have a combination, some statements may be

1:57:32
Invited.

1:57:41
Even. G. And,

1:57:58
So how to improve what you've got? Is three initially. And instead, so this is the specific set of stable. So cannot break in Guardian. This has a nationally to end table.

1:58:26
Because I conclude that the initially is true.

1:58:33
In that one, you know, and the state of those. So, therefore inviting to stay with the more and more

1:59:12
So the ensures few enough into this estimate is going to take us from 32, very, okay and see, stable and cheese. It doesn't change if you completed them. There's not like changing the whole class standing close and in this family. Meth you start with FIG So,

1:59:43
You need to look for things to be able to Of course in such a stable,

1:59:54
They tend to allow you to properties of that components to the, to the right. It's not big enough.

2:00:40
So, we're gonna have to for example soon.

2:00:58
The, some variety.

2:01:13
I wish I had a shirt like that. Targeted. Maybe have to concern.

2:02:09
Okay, so I have come by and and I have been charged.

2:02:23
It's actually.

2:02:27
And then I'm going to do the for

2:02:45
The. And,

2:03:42
I have this already. Unfortunately, I chose this corner to these contract. Mine general professional. And,

2:03:59
Feel good, man. So, what's happening here?

2:04:11
He goes from one to him. And what will we do? We helping I okay because I gave plus and plus one and you zero the next one. So, what's going to happen is that

2:04:35
And this two rows, right? This one, I'm basically I'm adding I

2:04:54
Right. Okay, guys, and I'm zeroing this

2:05:04
I don't know how things are going to schedule, so I can be selected anywhere because you see in case things. So I do one group to the next holder but I is anything else. So there I can be selected anymore. Anyway, the system once So zeros could mean things can be added anywhere.

2:05:33
Okay, so now we have a program C.

2:05:46
Now, we are so close to the border. Loads to make. Okay? So then I have a program.

2:05:58
He does exactly the same thing but words by the columns. So grave, next form.

2:06:30
Sign.

2:06:34
In box Jane between words.

2:06:46
And,

2:06:51
Dream.

2:07:07
Use came to J. Came between us.

2:07:35
So, this is exactly.

2:07:41
So okay.

2:07:47
One, I think, take us take easy organ. What we want to do is basically to combine our box.

2:08:06
The in based on my teach one does figure out whether condition is going to. Now the very first thing to check, I just programs compatible composition. Well, they have the same decoration, they have the same translation, therefore, that compact. The combined program would look exactly. Like this this and the signal contain this box.

2:08:45
So,

2:08:50
This is a different.

2:09:01
This is going to be fine as Sigma G.

2:09:12
DN.

2:09:20
I'm skipping the rain from the engine blind that I have the correct age. So what is this?

2:09:32
Some of the horrors is just as simple as the whole, but which some of which

2:09:44
Some of some of all the that is index. All those okay. And going to be.

2:10:10
You know, my

2:10:27
The more exp.

2:10:37
And,

2:10:47
Next.

2:11:12
Okay. So it's basically says, give me the lowest I such that everybody above me. Consume see wise basis and everything is zero down. So then we have no, this is if this is, I means this whole section here.

2:11:55
But this is noisy.

2:12:01
Now there could be zero rows here. The developer we just adds things and then on demand but this is a lowest number. The Anbridge Commission is here and do the same thing as J.

2:12:30
Is a lowest dream. We have which and we everything.

2:12:37
You know, if you think about this program of work, it's essentially things to remember. Yes, the sun senses progressing. Like this, his eye is J and then this moves over and eventually this moves over, it was over and 120 left to the end once ago.

2:13:07
Sound. That is not there. Everything for the right of it. Come colonizer zero entering below it, realizes on the Xbox One.

2:13:26
So we have this definition. So now that we have this definition, I can go back to the. You have a question. No. Okay. So then we can go back to the, to the, to programs and look at what properties they have. So, one property. So this is

2:13:49
One properties and variant as people.

2:14:00
Signals. Hi Jane things. So basically this says that the program does not change and total sum. There are no, the batteries in because S was initial, son. This is a car and think about. So in this environment, for instance, we could have statements that God says think take two points from one and added together and it's fine as long as the total substance cost.

2:14:44
When true let's do, I'm eventually all the rows except for one that was zeroed.

2:15:06
Understands that.

2:15:14
And I it's a number of should be able to tell that from the definition.

2:15:24
We also have a progress company, which says I equal x ensures I wonder more.

2:15:43
So if this is, I I point to this statement, corresponding to I and at this time it is, it's executed. It is currently that it's going to go on.

2:15:59
He wants them other things can happen here, but this is my gallery, never seen, no change on it. Way to change your eye using this statement.

2:16:19
You need, this has

2:16:24
Okay, and then we have stable high equal 1 and then when you variant

2:16:40
Price sigma, okay.

2:16:50
Takes the okay.

2:17:03
So that basic says that if you count on your own eyes, one loading, one zero row. Here, you have all these numbers, you get

2:17:22
Spring obvious that his property is home, right? Anybody has any questions? It's not do we have a ensure? Because we have an experiments. Right? Yeah. So one thing also, which one this eye to me, then I pointed this statement corresponding to, which is this where I say,

2:18:03
This, this statements are in that by eye, mmm, so I can say same in our street number four based on life or so, it's one specific statement. It's a one corresponding capital I which is a way soon. All okay.

2:18:33
Given this properties. We can write senior properties for us.

2:18:56
So excited for seeing this girl.

2:19:10
Has equal. Thanks, I'm Jane.

2:19:21
She doesn't change until some reason.

2:19:27
Okay, ingredient.

2:19:39
They would, why ensures he's more than why? Or more stable.

2:19:58
The price.

2:20:06
Things came one accomplish very similar. Kind of and approves of very much. Okay, so the question now becomes again, we can look at one program and have this properties verified and you can add other programs in the What can I tell?

2:20:44
So we're going to start that probably have to. So now I talk about are so, for instance, and we want to prove impatient as

2:21:23
Now, listening again, and to prove anybody, and we basically need an invalid in one program and stability in there. So so here we have any variant in this program and since he's anybody disabled, so that means that they can, they include that the property holds the cost, it's got to be treated is clear that it was programs, don't change the sound.

2:22:02
You could ever get a different answer, but technically, the way of prove it is, we use a new guardian and the instability

2:22:20
And I have to say, stable high, even one and

2:22:39
So, we have X stable, you see?

2:22:54
So if we have our here and this is true. I so this is seven, eight nine and everything. Here is zero.

2:23:13
This value came up exchanged by C. Why? Because seek and move on your values as a left.

2:23:29
And so it could make this road, shorter more zeros, but it would be a non-zero value. To the worst thing you can do is move everything to the first position here. And if that position one zero so I doesn't change. I still the last row beyond which everything is here.

2:23:55
Now, how do we know that this is?

2:24:24
What am I doing there? That could raise some issues.

2:24:33
So remember, this row has non-zeroes right the column program moves things to the left and I argue that it is not possible for this road to become the

2:24:59
Something that order.

2:25:04
She defends on.

2:25:08
Well, you had values to the left that value has to be something, right. She's arrogant values and still across the left in the system. However, if I have negative values, I can never seven and I minus seven and when they added all of something becomes a zero so it's on develop is zeroed so i is no stability.

2:25:39
So the proof would actually be fail if the I have to do a different proof, I can still do it but I can't. I can't do this property.

2:25:58
So, he seems to have the stability properties, then when I staple. Yeah, you know it's also stable in C but it's definitely boasts. It's stable because she's still before every house including one. So they would, you know, he wanted R and his table in for every value. You can see, therefore, it's also stable for running art and therefore, I instability in the composite.

2:26:35
And that's, that's a way to reason about the composition. So, without two properties here, we need to is proof. So, this

2:27:26
We we don't have to move the other conversation.

2:27:40
We don't have to use the very energy of this is enough and on the

2:28:02
This result follows from the food here or what? I mean you happen to approve. Just, we just stated the results of