# Thread: Automata Theory regular expressions

1. ## Automata Theory regular expressions

hello , hopefully i made this post in the right section lol. im trying to brush up on my automata for a test and i ran into something thats confusing me. this question asks

Which of the following regular expressions denotes the set of all strings over the alphabet {0,1} that contains at least one 0.
a) (1+0)*0(1+0)*
b) (1+0)*01*
c) 1*0(1+0)*
d) (1+0)*00*
e) 0*0(1+0)*
f) 1*00*
g) 0

now from what im seeing doesnt everyone of these choices contain atleast 1 zero? i dont know if maybe im reading the question wrong . i understand how to read the * and + but im not quite understanding what its asking. like for a) u can get 0 by itself, so thats atleast 1 zero. for b) u can get 0 alone, thats also atleast 1 zero.

2. ## Re: Automata Theory regular expressions

Hey zerocool18.

Does this mean the string is forced to have a 0 anywhere or in a specific way?

Looking at the question I'm inclined to agree with you but I should ask anyway.

3. ## Re: Automata Theory regular expressions

Originally Posted by chiro
Hey zerocool18.

Does this mean the string is forced to have a 0 anywhere or in a specific way?

Looking at the question I'm inclined to agree with you but I should ask anyway.
thats exactly how the question is worded. so im assuming that it can be anywere

4. ## Re: Automata Theory regular expressions

I thought so but I had to clarify.

Based on what you have stated every expression should have at least one zero (some many more).

I'm not sure how you could prove it but you could break up the strings in sub-strings and show them as a union of 0 terms and other arbitrary terms thus completing some sort of formal proof.

5. ## Re: Automata Theory regular expressions

Originally Posted by chiro
I thought so but I had to clarify.

Based on what you have stated every expression should have at least one zero (some many more).

I'm not sure how you could prove it but you could break up the strings in sub-strings and show them as a union of 0 terms and other arbitrary terms thus completing some sort of formal proof.
thanks i appreciate the help , atleast i know im on the right track lol