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Question

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Answers

Construct a Turing machine that computes the function $f\left(n_{1}, n_{2}\right)=\min \left(n_{1}, n_{2}\right)$ for all nonnegative integers $n_{1}$ and $n_{2} .$

As we all know that the thermal stability depends upon caramel. The stability depends upon the iconic character. The iconic get it did of the oxide of the oxide. So here the order will be weird. I know after that Cdo after that HD you because from Falling Skills Law, the electronic negativity of dead and 8 1.65 CD 1.69 and HDH two. Therefore, therefore later the electron negative of the matter more will be the eye. Any character. So here, in this problem of senses, correct?

Were asked to construct a Turing machine that computes the function F n equals n plus two for all non negative integers. And now, to construct this machine, we're going to use the unity notation. So this means that we haven't input, um n plus one ones. Then we should receive or should accept, this input and output. A tape which contains and plus two plus one, is equal to end plus three ones. So essentially, we want to add two more ones to this string. So there are some easy ways to do this for one starting out in state s zero. We know that for any non negative manager and the tape is going to contain at least 11 in the initial configuration and several want to take this one CS zero recognize it. And in the star configuration, this is the left most one. So let's move left and shift in. The state s one keep the one as is. And then once you've moved left, now we're reading a blank And so in state s one. If we read a blank, then you want to change this blank pinto a one constable shift in the state s to and we'll change this blanket. Draw one, and then we'll move left again. So you've added 11 so far. We want to add another one to this string. Do this will do the same thing. So what, You move left. We see that as to should recognize a blank here. And we want this blank to be changed into a once well, shifting to final state s three and changed the blank into a one. And although I used four states, this could actually be abbreviated. So instead of changing from state as Syria s one in the first place, I could have simply it started in state at zero. State and state at zero. Move the left. And then in state s zero, I encountered a blank. I would change to state s one. Change the blank toe one and move left. And then finally, in state s one. If I were to encounter a blank Kenwood, change the blank toe one and changing to the final state s to. And then we would obtain an output spring with a total of N plus three ones. So we'd obtained in unity notation the non negative imager and plus two

So for this question, we're told that eat picture frames is $46 we're also told that 10 picture frames it costs it is $55 for a cost. So first of all, we are asked to come up with an equation for our costs. So this is for part A. So the first thing we want to do this, they want to find her slope. So we know our slope is equal to 55 minus 46/10 minus eight. So that will get us nine over to as their slope. And so the next thing we need to do is we need to find our y intercept. So or RB So we have. Let's use 55 was our Y is equal to 9/2 pounds. 10 stories in this point over here plus B so that will get us 55 is equal to 45 plus B B is equal to 10. So you know that the equation for a line is why is able to 9/2 X plus 10. So the next thing we need to dio is we need to find this is for parts to be. We were asked to find her costs when making 20 picture frames. So we know we can just plug in 20 as our excellent say, why is it tonight over two times 20 plus 10 we can cancel out our to and this becomes a 10. So we can say this is equal to 90 plus time of which is people to 100. So their costs for making 20 picture frames is $100. First, See were asked how the picture friends can be made for a cost of $91. So we have 91 is equal to 9/2 x plus time which will get us 9/2 X is equal to 81. We can divide both sides by nine over to to get us accessible to 18. So we know that there are 18 fiction picture friends give me made for that cost When this is the answer for B and this is the answer for C and then for d were asked what our fist fixed costs. We know that this is simply our y intercept. So once again, our equation is why 0 to 9/2 x plus 10 from off first section parts A. And so you know, the hardest cases are Why intercept? So we never fixed Costs are $10 so these are answers.

Were asked to construct a Turing machine that computes the function f of N one and two equals and two plus two for all n. One and n two non negative integers. So recognize that input for this function, which is a pair and when end to is going to be a string which has and one plus one ones, followed by a star symbol, which separates the two components of the payer and then end to plus one one's for the second components and to you want to end up with End to Plus two plus one, which is, and two plus three ones as our output. This represents the non negative manager end two plus two. So we see that in our original input to the right of the asterisk we're being given and two plus one ones. So you want to add to ones to this somehow. One way to do this is to replace the aspirin with the one and then to replace the blank to the U right of our input with the one and then we'll have and two plus three ones. As long as we delete the first and one plus one ones And so this is actually a fairly simple machine to make. We're going to start out in the state s zero, and whenever we find a one in the States, we're going to delete it. Point it changes to a blink. We're going to stay in state s zero until eventually one state s zero and we reach the asterisk symbol. At this point, we're going to change the asterisk symbol to a one, and we're going to shift into State S one. And now, once we're in state s one, you want to move through the rest of the ones until we reach a blank in the first blank we reach. We want to change this into a one after shifting in the state s to. And so now our string has end two plus three ones. Exactly. And it doesn't have any asterisks separating any parts of the string and also s two is a final state, so this will be accepted by the machine. Now, this is one way to go about it. Another way is to actually, instead of having to go through all the ones we could back up after erasing the asterisk, complacent with the one. So you moved to the left, and then we don't have to worry about encounter in a one worm. Where in state s one. All we have to worry about is encountering that blank, which inevitably, Whoa! And then we want to change that blank into a one to changing into state s to We can move left or right.


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