Algorithm: BNF question

[jack223]

How do i get from 2 character words to 4 character words or 5 character words??
can anyone show me how to do that plz...

Q) Consider a language of words, where each word is a string of dots and dashes. The following grammar describes this language:

<word> ::= <dot> | <dash><word> | <word> <dot>
<dot> ::= .
<dash> ::= -

The meta-symbols of BNF are:

::= meaning “is defined as
| meaning is “or
<> angle brackets are used to surround category names

Question: List all strings with exactly three characters that are in this language?
Is the string ...---(three dots followed by three dashes) in this language?

Let's start listing the possible words. The only word consisting of one character is a single dot. By applying the second production rule, you can add a dash in front of the word, which gives you <dash> <dot>. If you apply the third rule instead, you add a dot after the first dot, resulting in <dot> <dot>.

So now I have two valid words consisting of two characters each:

-.
..

Now I can go on and apply the two production rules again to these two words, resulting in four three-character words. Of course, in the same way, you get 8 four-character words, 16 five-character words and so on.

How do I apply the production rule to get to the four 3 character word??

[agiorgio]

I came up with three three-character words:

...
-..
--.

I don't see how to create the fourth one.

[jack223]

I came up with three three-character words:

...
-..
--.

I don't see how to create the fourth one.

That's what I got too....the fourth one is "-.." which already exist so it doens't count.

I have another question and this one is little harder.

<S> = a<S>a | b<S>b | a | b

Q: list all the 5-character strings that are in this language?

My answer is there are four 5-character strings in this language and they are "ababa" , "abbba" , "baaab" , "babab".....is this right??

<S> = a<S>a
<S> = b<S>b
<S> = a
<S> = b

so therefore, <S> = ab<S>ba = ababa or abbba

and <S> = b<S>b = ba<S>ab = baaab or babab