1. Describe the strings that are represented by the regular expression R*( (E|e) (+ | -)? R R*)?

where, R = {0, 1, 2, ..., 9}

2. What languages do a*|b* and (a* b)* denote.

3. How many strings are present in (a* b)* but not in (a+ b)*. If there are multiple such strings, can you describe them in plain English. (Note: a+ indicates kleene plus operator)

4. How many strings are present in a(a | b)* but not in aa(a | b)*. If there are multiple such strings, can you describe them in plain English.

5. Simplify each regular expressions:

a) | ab | abab(ab)*

b) aa(b*|a)|a(ab*|aa)

6. Refer to the regular expression studied in class to generate all strings with even number of as and any number of bs. Give a regular expression which consists of odd number of as.