# key6sp00 - COT3100 Spring 2000 S Lang Solution Key to...

This preview shows pages 1–2. Sign up to view the full content.

COT3100, Spring 2000 S. Lang Solution Key to Assignment #6 (Optional) 4/24/2000 1. Give a regular expression for each of the following languages (no proof or explanation is required): (a) The set of strings over { a , b } that do not contain the substring ba and do not contain the substring ab . a * + b *. (Intuitively, this answer is because the set contains strings λ , a , aa , aaa , …, b , bb , bbb , etc. That is, the set contains symbols a ’s by themselves, or symbol b ’s by themselves, but never a and b mixed together.) (b) The set of strings over { a , b } that have a length divisible by 3. (( a + b )( a + b )( a + b ))*, i.e., ( aaa + aab + aba + abb + baa + bab + bba + bbb )*. (c) The set of strings over { a , b , c } that have exactly two occurrences of symbol a (no restrictions on th occurrences of symbols b or c ). ( b + c )* a ( b + c )* a ( b + c )*. 2. Prove the following identities of regular expressions using appropriate rules and properties. Explain each step of your proof. (a) ( a + b )* a * = ( a * + b )*. Note that ( a * + b )* = ( a + b )*, using the rule ( u + v )* = ( u * + v )* with u = a and v = b = ( a + b )* λ , because the rule u λ = u ( a + b )* a *, because λ a *

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern