# Thread: regular expressions help

1. ## regular expressions help

Well I’m studying for my Languages and Automata class and I do not understand a few examples regarding certain regular expressions:

In each example assume that the alphabet ∑ is {0,1}

1. ( ∑∑ )* = {w|w is a string of even length}
I don’t follow this…I can rewrite this to: ({0,1}{0,1})*, and this would imply that the language consists of all possible pairs of 0s and 1s.

2. ( ∑∑∑ )* = {w|the length of w is a multiple of three}
This one is similar to the one above, I simply don’t get it.

3. (0∑*0) U (1∑*1) U (0) U (1) = {w|w starts and ends with the same symbol}
I tried dissecting this one, but I still don’t understand: (0∑*0) means all strings that begin and end with 0; (1∑*1) – all strings that begin and end with 1; so how does the rest of the expression ‘U (0) U (1)’ make the first and last symbol the same?

Any help will be appreciated. Man, this will be one “fun” class….

2. I read my own post...and now I get the first two examples. The whole bit about "all possible pairs of 0s and 1s." makes the string even...duh (see, its always good to write your own thoughts down, they start making sense - sometimes). And number two is the same thing, but instead of a pair we have a triple.

But the third example is still confusing...

3. someone has explained the examples to me via reputation, but did not leave a name, so I don't know whom to thank...I'm not sure who it was, but am leaning towards webmaster.

well, whoever it was, thank you very much!

4. ...and for those of us who are still curious about number 3.... how bout a quick explanation of how that can end in 0 or start in 1.

i havent taken any Language and Automata courses yet, seems interesting though.

5. well the unions with the sets {0} and {1} are made in case the string consists of only one 1 or one 0 - in that case it starts, and ends, with the same character

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