November 13, 1995

		cs330 - Discrete Structures
		===========================
		          Fall 1995


Homework #5
Due: November 22

Exercise	Points
----------------------
1		20
2		15
3		30
4		20
5		 5
6		15
----------------------
	Total  105

1) Let L={E, abb, b} and M={bba, ba, b}. Evaluate the following
language expressions.
a) LM
b) ML
c) L^2
d) M^3

2) Use your wits to find the unknown language L in each of the following
language equations.
a) {E, a, ab}L = {b, ab, ba, aba, abb, abba}
b) L{a, b} = {a, baa, b, bab}
c) L{E, a} = {E, a, b, ab, ba, aba}

3. Describe the language for each of the following regular expressions.
a) a + b
b) a + bc
c) a + b*
d) ab* + c
e) ab* + bc*
f) a*bc* + ac

4. Find a regular expression to describe each of the following
languages.
a) {a, b, c}
b) {a, aaa, aaaaa, aaaaaaa, ...}	odd number of a
c) (a^m)b(c^n)	with m and n natural numbers
d) {E, a, b, c, aa, bb, cc, aaa, bbb, ccc, .., a^n, b^n, c^n, ...}

5) Find a regular expressin over the alphabet {0, 1} to describe the
set of all binary numerals without a leading 0 (except for 0 itself).

6) Find a regular expression for over the alphabet {a, b} to describe
each of the following languages.
a) strings with even length
b) strings containing the substring aba
c) strings with an odd number of a's.

Please remember to print your name on the front page of your work,
together with your SSN.