# Homework Help: Weird :S

1. Mar 26, 2006

### prevail

Let $$\Sigma$$ = {$$\beta$$,x,y,z} where $$\beta$$ denotes a blank, so x$$\beta \neq$$ x, $$\beta \beta \neq \beta$$, and x$$\beta$$y $$\neq$$ xy but x $$\lambda$$y = xy.

Compute each of the following:

1: $$\parallel \lambda \parallel$$
2: $$\parallel \lambda \lambda \parallel$$
3: $$\parallel \beta \parallel$$
4: $$\parallel \beta \beta \parallel$$
5: $$\parallel \beta$$3 $$\parallel$$
6: $$\parallel$$ x $$\beta \beta$$ x $$\parallel$$
7: $$\parallel \beta \lambda \parallel$$
8: $$\parallel \lambda$$ 10 $$\parallel$$

Uhm.. can someone help me out ? I've tried like 3 days now (without progress).

2. Mar 26, 2006

### Tom Mattson

Staff Emeritus
What have you done so far?

3. Mar 27, 2006

### prevail

Well.. the problem is that i'm totally stuck. I have no idea what to do.. I've red the chapter over and over, checked several math websites, forum and so on..

It seems to me that people find it difficult to solve this no matter math skills

So if you don't want to help me (the assigment was handed in today).. that's ok. I can go on not understanding this..

4. Mar 29, 2006

### prevail

I'm surprised that nobody can solve this ......

5. Mar 29, 2006

### HallsofIvy

You haven't given a whole lot of information! You said $\beta$ represents a blank (I guess we might call that a "hard" blank) so really is treated just as another symbol. But what is $\lambda$? The only thing you tell us about that is "but x$\lambda$y= xy". So $\lambda$ is a "soft" blank- like nothing? Is $\beta^3$ the same as $\beta\beta\beta$? And what, exactly is the definition of $\parallel \parallel$? It would guess it is the length of the string but it would be a good idea to say that explicitely.

6. Mar 29, 2006

### prevail

$$\lambda$$ is according to definition a empty string - that is, the string consisting of no symbols taken from $$\Sigma$$.

$$\{ \lambda \} \neq \emptyset$$ because $$| \{ \lambda \} | =$$ 1 $$\neq$$ 0 $$= | \emptyset |$$.

$$\parallel$$ w $$\parallel[/itex] = the length of w, and [tex] \parallel \lambda \parallel$$ = 0. $$\parallel \beta \parallel$$ = 1. ...

Sorry for the lack of information..

Last edited: Mar 29, 2006
7. Mar 29, 2006

### prevail

Some of them are obvious...

8. Mar 29, 2006

### HallsofIvy

Indeed all of them are obvious. It's just counting!
1.$$\parallel \lambda \parallel= 0$$

2.$$\parallel \lambda \lambda\parallel= 0$$

3.$$\parallel \beta \parallel= 1$$

4.$$\parallel \beta^3= 3$$

.
.
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8. $$\parallel \lambda^{10}= 0$$

9. Apr 1, 2006

### prevail

So.. nr 6 is like.. 4, right?

10. Apr 1, 2006

### HallsofIvy

Yes, that is correct- just count the number of symbols in the string.

11. Apr 1, 2006

### prevail

aight, thanks for the help dude