CS-520  Introduction to Formal Models  Fall 1997

Homework 1

This homework is due in class on September 10. Each problem is worth 10 points.

1. On a page separate from the remaining problems, attach a photo of yourself. Write your name next to the photo. Underneath the photo, write 1-2 sentences describing why you are taking this course and what you would like to learn from it. If you like, please also describe a little about yourself and your interests.

Your page will be photocopied and returned to you with the rest of the homework.

2. Give regular expressions for the languages described in Exercise 1.4 page 84 parts b,f and l. You don’t need to include proofs that your regular expressions are correct. (However it is a good idea to at least check your expressions on several examples before handing them in.)

3. Let R be a regular expression that describes the language of strings with an even number of 0’s and an even number of 1’s. For example, R could be:

(00 ∪ 11 ∪ (01 ∪ 10)(00 ∪ 11)^{∗}(01 ∪ 10))^{∗}

Explain why the following regular expression describes the language of strings with an even number of 0’s and an odd number of 1’s:

R(1 ∪ 01(11)^{∗}0)R